Browsing Combinatorics and Optimization by Subject "directed graph"
Now showing items 1-4 of 4
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Approximation Algorithms for (S,T)-Connectivity Problems
(University of Waterloo, 2010-08-03)We study a directed network design problem called the $k$-$(S,T)$-connectivity problem; we design and analyze approximation algorithms and give hardness results. For each positive integer $k$, the minimum cost $k$-vertex ... -
A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number
(Elsevier ScienceDirect, 2023-01)We prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with ... -
On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture
(Elsevier, 2021-05-01)For a digraph G and v is an element of V(G), let delta(+)(v) be the number of out-neighbors of v in G. The Caccetta-Haggkvist conjecture states that for all k >= 1, if G is a digraph with n = |V(G)| such that delta(+)(v) ... -
Packing Directed Joins
(University of Waterloo, 2004)Edmonds and Giles conjectured that the maximum number of directed joins in a packing is equal to the minimum weight of a directed cut, for any weighted directed graph. This is a generalization of Woodall's Conjecture ...