Hemanshu Kaul

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Let G1 and G2 be graphs of order n with maximum degree ∆1 and ∆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 ∆1∆2 < n 2 , then G1 and G2 pack. We extend this result by showing that if ∆1∆2 ≤ n2 , then G1 and(More)
An n-tuple π (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 π. 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.(More)
The distinguishing chromatic number χD (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 χ(·). Our(More)
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, Bollobás and Eldridge, and independently Catlin, conjectured that if (∆(G1)+1)(∆(G2)+1)≤ n+1, then G1 and G2 pack. Towards this conjecture, we show that for ∆(G1),∆(G2)≥ 300, if(More)
Single and combined applications of three sprout inhibitors, maleic hydrazide (MH), isopropyl 3-chlorophenylcarbamate (CIPC) and isopropyl phenylcarbamate (IPC) mixed with CIPC in a commercial formulation coded AMK (Tixit-C, Sandoz, S.A.E., Barcelona, Spain; 2.0% IPC +0.7% CIPC) were tested on potatoes stored from March to June under ambient conditions(More)
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 that(More)