Browsing University of Waterloo by Author "Hompe, Patrick"
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Concatenating Bipartite Graphs
Chudnovsky, Maria; Hompe, Patrick; Scott, Alex; Seymour, Paul; Spirkl, Sophie (The Electronic Journal of Combinatorics, 2022)Let x, y E (0, 1], and let A, B, C be disjoint nonempty stable subsets of a graph G, where every vertex in A has at least x |B| neighbors in B, and every vertex in B has at least y|C| neighbors in C, and there are no edges ... -
A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number
Carbonero, Alvaro; Hompe, Patrick; Moore, Benjamin; Spirkl, Sophie (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 ... -
Cycles and coloring in graphs and digraphs
Hompe, Patrick (University of Waterloo, 2022-08-22)We show results in areas related to extremal problems in directed graphs. The first concerns a rainbow generalization of the Caccetta-H\"{a}ggkvist conjecture, made by Aharoni. The Caccetta-H\"{a}ggkvist conjecture states ... -
Digraphs with All Induced Directed Cycles of the Same Length are not → χ -Bounded
Carbonero, Alvaro; Hompe, Patrick; Moore, Benjamin; Spirkl, Sophie (2022-10-07)For t > 2, let us call a digraph D t-chordal if all induced directed cycles in D have length equal to t. In an earlier paper, we asked for which t it is true that t-chordal graphs with bounded clique number have bounded ... -
On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture
Hompe, Patrick; Pelikánová, Petra; Pokorná, Aneta; Spirkl, Sophie (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) ...