Browsing Waterloo Research by Subject "directed graph"
Now showing items 1-2 of 2
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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) ...