# Hemanshu Kaul

• Combinatorics, Probability & Computing
• 2007
Let G1 and G2 be graphs of order n with maximum degree âˆ†1 and âˆ†2, respectively. G1 and G2 are said to pack if there exist injective mappings of the vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer showed that if âˆ†1âˆ†2 < n 2 , then G1 and G2 pack. We extend this result by showing that if âˆ†1âˆ†2 â‰¤ n2 , then G1 andâ€¦ (More)
• Journal of Graph Theory
• 2012
An n-tuple Ï€ (not necessarily monotone) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} in which the degree of vi is the ith entry of Ï€. Graphic n-tuples (d (1) 1 , . . . , d (1) n ) and (d (2) 1 , . . . , d (2) n ) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that dG1(vi) = d (1) i and dG2(vi) = d (2) i for all i.â€¦ (More)
• SIAM J. Discrete Math.
• 2010
The distinguishing chromatic number Ï‡D (G) of a graph G is the least integer k such that there is a proper k-coloring of G which is not preserved by any nontrivial automorphism of G. We study the distinguishing chromatic number of Cartesian products of graphs by focusing on how much it can exceed the trivial lower bound of the chromatic number Ï‡(Â·). Ourâ€¦ (More)
• Combinatorica
• 2008
Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets are disjoint. In 1978, BollobÃ¡s and Eldridge, and independently Catlin, conjectured that if (âˆ†(G1)+1)(âˆ†(G2)+1)â‰¤ n+1, then G1 and G2 pack. Towards this conjecture, we show that for âˆ†(G1),âˆ†(G2)â‰¥ 300, ifâ€¦ (More)
• Comp. Opt. and Appl.
• 2007
Simultaneous generalized hill climbing (SGHC) algorithms provide a framework for using heuristics to simultaneously address sets of intractable discrete optimization problems where information is shared between the problems during the algorithm execution. Many well-known heuristics can be embedded within the SGHC algorithm framework. This paper shows thatâ€¦ (More)