Sean Kim

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math.CO2025

A Note on Large Degenerate Induced Subgraphs in Sparse Graphs

Alexander Clow, Sean Kim, Ladislav Stacho

Given a graph $G$ and a non-negative integer $d$ let $α_{d} (G)$ be the order of a largest induced $d$ -degenerate subgraph of $G$ . We prove that for any pair of non-negative integers…

math.CO2023

4-Chromatic Graphs Have At Least 4 Cycles of Length $0 mod 3$

Sean Kim, Michael E. Picollelli

A 2018 conjecture of Brewster, McGuinness, Moore, and Noel asserts that for $k \geq 3$ , if a graph has chromatic number greater than $k$ , then it contains at least as many cycles of…

A Note on Large Degenerate Induced Subgraphs in Sparse Graphs

4-Chromatic Graphs Have At Least 4 Cycles of Length 0mod3

4-Chromatic Graphs Have At Least 4 Cycles of Length $0 mod 3$