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Krausz dimension and its generalizations in special graph classes
Krausz dimension intersection graphs linear k-uniform hypergraphs chordal graphs polar graphs
2011/9/14
Abstract: A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in com...
Agoh's conjecture: its proof, its generalizations, its analogues
Agoh's conjecture its generalizations its analogues Number Theory
2011/9/9
Abstract: In this paper we formulate some generalizations of Agoh's conjecture. We provide a proof of one of them. We also formulate conjectures involving congruence modulo primes about hyperbolic sec...
Commutativity degree, its generalizations, and classification of finite groups
Commutativity degree generalizations classification of finite groups
2010/12/14
Classification of finite groups is a central problem in theory of groups.Even though finite abelian groups have been completely classified, a lot still remains to be done as far as non-abelian groups ...
Some Problems and Solutions Involving Mathieu's Series and Its Generalizations
Mathieu's series Integral representations Bessel functions Hypergeometric functions One-sided inequalities Fourier transforms Riemann and Hurwitz Zeta Eulerian integral
2008/6/26
The authors investigate several recently posed problems involving the familiar Mathieu series and its various generalizations. For certain families of generalized Mathieu series, they derive a number ...