Hemanshu Kaul

Packing of graphic n -tuples

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, …, d) and (d, …, d) pack if there are edge-disjoint n-vertex graphs G1 and G2 such that d(vi) = d and d(vi) = d for all i. We prove that graphic n-tuples π1 and π2 pack if , where Δand δdenote the largest and smallest entries in π1 + π2 (strict inequality when δ = 1); also, the bound is sharp. Kundu and Lovasz independently proved that a graphic n-tuple π is realized by a graph with a k-factor if the n-tuple obtained by subtracting k from each entry of π is graphic; for even n we conjecture that in fact some realization has k edge-disjoint 1-factors. We prove the conjecture in the case where the largest entry of π is at most n/2 + 1 and also when k⩽3.

Extremal Graphs for a Graph Packing Theorem of Sauer and Spencer

Let G1 and G2 be graphs of order n with maximum degree Δ1 and Δ2, 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 Δ1Δ2 < n/2, then G1 and G2 pack. We extend this result by showing that if Δ1Δ2 < n/2, then G1 and G2 do not pack if and only if one of G1 or G2 is a perfect matching and the other either is Kn/2·n/2 with n/2 odd or contains Kn/2 + 1.

Distinguishing Chromatic Number of Cartesian Products of Graphs

The distinguishing chromatic number

Global optima results for the Kauffman NK model

\chi_{_D}(G)

On a graph packing conjecture by Bollobás, Eldridge and Catlin

of a graph

New global optima results for the Kauffman NK model: handling dependency

G

New Methodology for Transportation Investment Decisions with Consideration of Project Interdependencies

is the least integer

Analyzing the performance of simultaneous generalized hill climbing algorithms

k

Maximum Series-Parallel Subgraph

such that there is a proper

Long Local Searches for Maximal Bipartite Subgraphs

k