Recent Journal Publications (most recent first)
- J. L. Gross, I. F. Khan, T. Mansour, and T. W. Tucker,
Calculating genus polynomials via string operations and matrices,
manuscript (2016), 28 pages.
- J. L. Gross, T. Mansour, and T. W. Tucker,
Valence-partitioned genus polynomials and their application to generalized dipoles,
Australasian Journal of Combinatorics, to appear.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Root geometry of polynomial sequences II: Type (1,0),
Journal of Mathematical Analysis and Applications 441 (2016), 499-528.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Iterated claws have real-rooted genus polynomials,
Ars Mathematica Contemporanea 10 (2016), 255-268.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Combinatorial conjectures that imply local log-concavity of grap[h genus polynomials,
European Journal of Combinatorics 52 (2016), 207-222.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Root geometry of polynomial sequences I: Type (0,1),
Journal of Mathematical Analysis and Applications 433 (2016), 1261-1289.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Log-concavity of the genus polynomials of Ringel ladders,
Electronic Journal of Graph Theory and Applications 3 (2015), 109-126.
- Y. Chen, J. L. Gross, and T. Mansour,
Log-concavity of genus distributions for circular ladders,,
Mathematische Nachrichten 288 (2015), 1952-1969.
- E. Akleman, J. Chen, and J. L. Gross,
Extended graph rotation systems as a model for cyclic weaving on orientable surfaces,
Discrete Applied Mathematics 193 (2015), 61-79.
- J. L. Gross, T. Mansour, T. W. Tucker, and D. G-L. Wang,
Log-concavity of combinations of sequences and applications to genus distributions,,
SIAM Journal of Discrete Mathematics 29 (2015), 1002-1029.
- E. Akleman, J. Chen, and J. L. Gross,
Block meshes: topologically robust shape modeling with graphs embedded on 3-manifolds,,
Computers and Graphics 14 (2015), 306-326.
- J. L. Gross, T. Mansour, and T. W. Tucker,
Log-concavity of the genus polynomials for a sequence of cubic Halin graphs,,
Journal of Combinatorics 5 (2014), 203-233.
- J. L. Gross, M. Kotrbcik, and T. Sun
Genus distributions of cubic series-parallel graphs,,
Discrete Mathematics and Theoretical Computer Science 16 (2014), 129-146.
- J. L. Gross, T. Mansour, and T. W. Tucker
Log-concavity of genus distributions of ring-like families of graphs,,
European Journal of Combinatorics 42 (2014), 74-91. Online June 2014.
- J. L. Gross, I. F. Khan, and M. I. Poshni,
Genus distributions for iterated claws,
Electronic Journal of Computing 21 (2014), #P1.12.
- M. I. Poshni, I. F. Khan, and J. L. Gross,
Genus distributions of iterated 3-wheels and 3-prisms,
Ars Mathematica Contemporanea 7 (2014), 423-440. Online December 2013.
- J. L. Gross,
Embeddings of graphs of fixed treewidth and bounded degree,
Ars Mathematica Contemporanea 7 (2014), 379-403.
Presented at Special Session on Topological Graph Theory,
annual national meeting of the Amer. Math.Soc., Boston, Jan 2012. Online Dec 2013.
- Y. Chen, J. L. Gross, and X. Hu,
Enumeration of digraph embeddings,
European Journal of Combinatorics 36 (2014), 660-678. Online October 2013.
- Y. Chen, J. L. Gross, and T. Mansour,
Total embedding distributions of circular ladders,,
Journal of Graph Theory 74 (2013), 32-57. Online August 2012.
- J. L. Gross,
Embeddings of cubic Halin graphs: genus distributions,,
Ars Mathematica Contemporanea 6 (2013), 37-56.
Keynote presentation at Bled'11--7th Slovenian International Conference on Graph Theory, June 2011.
Online June 2012.
- Y. Chen, J. L. Gross, and T. Mansour,
Genus distributions of starladders,
Discrete Mathematics 312 (2012), 3059-3067. Online 2012.
- I. F. Khan, M. I. Poshni, and J. L. Gross,
Genus distribution of P3 x Pn,
Discrete Mathematics 312 (2012), 2863-2871. Online July 2012.
- S. Hu, Q. Xing, E. Akleman, J. Chen, and J. L. Gross,
Pattern mapping with quad-pattern-coverable quad-meshes,
Computers and Graphics 36 (2012), 455-465. Online April 2012.
- M. I. Poshni, I. F. Khan, and J. L. Gross,
Genus distribution of graphs under self-edge-amalgamations,
Ars Mathematica Contemporanea 5 (2012), 127-148.
- M. I. Poshni, I. F. Khan, and J. L. Gross,
Genus distributions of 4-regular outerplanar graphs,
Electronic Journal of Combinatorics 18 (2011), #P212.
- J. L. Gross,
Genus distributions of cubic outerplanar graphs,
Journal of Graph Algorithms and Applications 15 (2011), 295-316.
- E. Akleman, J. Chen, Y-L Chen, Q. Xing, and J. L. Gross,
Cyclic twill-woven objects,
Computers and Graphics, 35 (2011), 623-631.
- J. L. Gross,
Genus distributions of graph amalgamations: Self-pasting at root-vertices,
Australasian Journal of Combinatorics 49 (2011), 19-38.
- I. F. Khan, M. I. Poshni, and J. L. Gross,
Genus distribution of graph amalgamations: Pasting when one root has arbitrary degree,
Ars Mathematica Contemporanea 3 (2010), 121-138.
- J. L. Gross,
Genus distribution of graphs under surgery: Adding edges and splitting vertices,
New York Journal of Mathematics 16 (2010), 161-178.
This paper is available via http://nyjm.albany.edu/j/2010/16-9.html.
- J. L. Gross and T. W. Tucker,
A Celtic framework for knots and links,
Discrete and Computational Geometry 46 (2011), 86-99. (online March 2010)
- M. I. Poshni, I. F. Khan, and J. L. Gross,
Genus distribution of graphs under edge-amalgamations,
Ars Mathematica Contemporanea 3 (2010), 69-86.
- J. L. Gross, I. F. Khan, and M. I. Poshni,
Genus distribution of graph amalgamations: Pasting at root-vertices,
Ars Combinatoria 94 (2010), 33-53.
- E. Akleman, J. Chen, Q. Xing, and J. L. Gross,
Cyclic plain-weaving on polygonal mesh surfaces with extended graph rotation systems,
ACM Trans. on Graphics 28 (2009), Article #78 (from SIGGRAPH 2009).
Recent Refereed or Invited Conference Publications (most recent first)
- J. L. Gross, T. Mansour, T. W. Tucker, D. G. L. Wang, Log-concavity of combinations of sequences and applications to genus distributions, Invited presentation at Special Session on Topological Graph Theory, annual national meeting of the Amer. Math. Soc, Baltimore, January 2014.
- J. L. Gross, All graph genus distributions are log-concave. and related conjectures, Invited presentation at Special Session on Graph Theory Conjectures, annual national meeting of the Amer. Math. Soc, Baltimore, January 2014.
- J. L. Gross, T. Mansour, T. W. Tucker, D. G. L. Wang, Iterated claws have real-rooted genus polynomials, keynote presentation at GEMS'13--Smolenice, Slovakia, July 2013.
- J. L. Gross, Genus distributions algorithm for fixed treewidth and bounded degree,
Ars Mathematica Contemporanea 7, 379-403. Invited presentation at Special Session on Topological Graph Theory, annual national meeting of the Amer. Math. Soc, Boston, January 2012.
- S. Hu, Q. Xing, E. Akleman, J. Chen, and J. L. Gross, Pattern mapping with quad-pattern-coverable quad-meshes, 2011 IEEE International Conference on Shape Modeling and Applications (SMI'12), June, 2012.
- J. L. Gross, Embeddings of cubic Halin graphs: genus distributions, keynote presentation at Bled'11--7th Slovenian International Conference on Graph Theory, June 2011.
- E. Akleman, J. Chen, Y-L Chen, Q. Xing, and J. L. Gross, Cyclic twill-woven objects, 2011 IEEE International Conference on Shape Modeling and Applications (SMI'11), June, 2011.
- Q. Xing, E. Akleman, J. Chen, and J. L. Gross, Single-cycle plain-woven objects, 2010 IEEE International Conference on Shape Modeling and Applications (SMI'10), 90-99. June, 2010.
- E. Akleman, J. Chen, and J. L. Gross, Paper-strip sculptures, 2010 IEEE International Conference on Shape Modeling and Applications (SMI'10), 136-140. June, 2010.
- E. Akleman, J. Chen, Q. Xing, and J. L. Gross, Cyclic plain-weaving on polygonal mesh surfaces with extended graph rotation systems, Article #78, SIGGRAPH. August, 2009.
Some Older Publications in Topological Graph Theory (oldest first)
- Branched coverings of graph imbeddings (with S. R. Alpert), Bull. Amer. Math. Soc. 79 (1973), 942-945.
- The topological theory of current graphs (with S. R. Alpert), J. Combinatorial Theory B 17 (1974), 218-233.
- Voltage graphs, Discrete Mathematics 9 (1974), 239-246.
- Riemann surfaces and the general utilities problem, Basic Questions of Design Theory, (ed. W. R. Spillers), 383-394, North-Holland, Amsterdam, 1974.
- Quotients of complete graphs: Revisiting the Heawood map-coloring problem (with T. W. Tucker), Pacific J. Math. 55 (1974), 391-402.
- The genus of nearly complete graphs-Case 6, Aequationes Math. 13 (1975), 243-249.
- Graph imbedding problems (with S. R. Alpert), Amer. Math. Monthly 82 (1975), 835-837.
- Components of branched coverings of current graphs (with S. R. Alpert), J. Combinatorial Theory B 20 (1976), 283-303.
- Every connected regular graph of even degree is a Schreier coset graph, J. of Combinatorial Theory 22 (1977), 227-232.
- Generating all graph coverings by permutation voltage assignments (with T. W. Tucker), Discrete Mathematics 18 (1977), 273-283.
- Imbeddings of metacyclic Cayley graphs, Theory and Applications of Graphs (Lecture Notes in Math., Vol. 642) ed. Y. Alavi and D. R. Lick, Springer-Verlag, Berlin, 1978, 194-203.
- An infinite family of octahedral crossing numbers, J. Graph Theory 2 (1978), 171-178.
- Fast computations in voltage graph theory (with T. W. Tucker), Ann. NY Acad. Sci. 319 (1979), 247-253.
- Local maxima in graded graphs of imbeddings (with T. W. Tucker), Ann. NY Acad. Sci. 319 (1979), 254-257.
- A linear time planarity algorithm for 2-complexes (with R. H. Rosen), J. ACM 26 (1979), 611-617.
- A determination of the toroidal K-metacyclic groups (with S. J. Lomonaco), J. Graph Theory 2 (1980), 165-172.
- Some problems in topological graph theory (with F. Harary), J. Graph Theory 4 (1980), 253-263.
- A combinatorial characterization of planar 2-complexes (with R. H. Rosen), Colloquium Mathematicum 44 (1981), 241-247.
- Hierarchy for imbedding-distribution invariants of a graph (with M. Furst), J. Graph Theory 11 (1987), 205-220.
- Finding a maximum-genus graph imbedding (with M. Furst and L. McGeoch), J. ACM 35 (1988), 523-534.
- Genus distribution for two classes of graphs (with M. Furst and R. Statman), J. Combinatorial Theory B 46 (1989), 22-36.
- Genus distributions for bouquets of circles (with D. P. Robbins and T. W. Tucker), J. Combinatorial Theory B 47 (1989), 292-306.
- Local extrema in genus-stratified graphs (with R. G. Rieper), J. Graph Theory 15 (1991), 159-171.
- Limit points for average genus, (I): 3-connected and 2-connected simplicial graphs (with J. Chen), J. Combinatorial Theory B 55 (1992), 83-103.
- Limit points for average genus (II): 2-connected non-simplicial graphs (with J. Chen), J. Combinatorial Theory B 56 (1992), 108-129.
- Kuratowski-type theorems for average genus (with J. Chen), J. Combinatorial Theory B 57 (1993), 100-121.
- On the average genus of a graph (with E. W. Klein and R. G. Rieper), Graphs and Combinatorics 9 (1993), 153-162.
- Overlap matrices and total imbedding distributions (with J. Chen and R. G. Rieper), Discrete Math 128 (1994), 73-94.
- Extending a graph browser for topological graph theory (with J. I. Helfman), Proceedings of the DIMACS Workshop on Computational Support for Discrete Mathematics (at Rutgers, March 1992; eds. N. Dean and G. E. Shannon), Vol. 15 of DIMACS Series in Discrete Math. and Theoretical Comp. Sci., American Mathematical Society, 1994.
- No lower limit points for average genus (with J. Chen), Proceedings of the 7th Quadrennial International Conference on the Theory and Application of Graphs (ed. Y. Alavi and A. Schwenk), Wiley-Interscience 1995, 183-194.
- Voltage graphs for parallel architecture layouts (with J. Chen), Proceedings of the 7th Quadrennial International Conference on the Theory and Application of Graphs (ed. Y. Alavi and A. Schwenk), Wiley-Interscience 1995, 455-466.
- Lower bounds for the average genus (with J. Chen and R. G. Rieper), J. Graph Theory 19 (1995), 281-296.
- Stratified graphs for imbedding systems (with T. W. Tucker), Discrete Math 143 (1995), 71-86.
- Maximum genus and connectivity (with J. Chen and D. Archdeacon), Discrete Math. 149 (1996), 19-30.
- Algebraic specification of interconnection networks by permutation voltage graph morphisms (with J. Chen), Mathematical Systems Theory 29 (1996), 451-470.
- A tight lower bound on the maximum genus of a simplicial graph (with J. Chen and S. Kanchi), Discrete Math 156 (1996), 83-102.
Some Older Publications in 3-Dimensional Topology (oldest first)
- Manifolds in which the Poincare conjecture is true, Trans. Amer. Math. Soc. 142 (1969), 177-189.
- A unique decomposition theorem for 3-manifolds with connected boundary, Trans. Amer. Math. Soc. 142 (1969), 191-199.
- The decomposition of three-manifolds with several boundary components, Trans. Amer. Math. Soc. 147 (1970), 561-572.
- An infinite class of irreducible homology 3-spheres, Proc. Amer. Math. Soc. 25 (1970), 173-176.
- Prime 3-manifolds and the doubling operation, Proc. Amer. Math. Soc. 27 (1971), 375-380.
Some Older Publications on Graph Algorithms (oldest first)
- Fast computations in voltage graph theory (with T. W. Tucker), Ann. NY Acad. Sci. 319 (1979), 247-253.
- A linear time planarity algorithm for 2-complexes (with R. H. Rosen), J. ACM 20 (1979), 611-617.
- A combinatorial characterization of planar 2-complexes (with R. H. Rosen), Colloquium Mathematicum 44 (1981), 241-247.
- Finding a maximum-genus graph imbedding (with M. Furst and L. McGeoch), J. ACM 35 (1988), 523-534.
Some Older Publications in Sociometrics for Anthropology (oldest first)
- Food and culture: Measuring the intricacy of rule systems (with M. Douglas), Social Science Information (SAGE, London and Beverly Hills) 20 (1981), 1-35.
- Graph-theoretical model of social organization, Annals of Discrete Mathematics 13 (1982), 81-88.
- Information-theoretic scales for cultural rule systems, Chapter 8 of Sociological Methodology 1983-1984 (ed. S. Leinhardt), 248-271.
- Measurement of calendrical information in food-taking behavior. Chapter 5 of Food in the Social Order, (ed. Mary Douglas) Russell Sage Foundation, New York, 1984.
- Measuring Culture: A Paradigm for the Analysis of Social Organization (with S. F. Rayner), Columbia University Press, New York, 1985.