Matthew P. Yancey

activity

20122026

most citedPlanar 4-critical graphs with four triangles

19 citations · 60 across the 17 of their papers we have counts for

collaborators

20 papers

math.CO2026

Resolving the Kohayakawa--Kreuter Conjecture for Families

Matthew Yancey

A graph $G$ is $(a, b)$ -sparse if every nonempty subgraph $H$ satisfies $e (H) \leq a v (H) - b$ . We are interested in the conditions under which an $(a, b)$ -sparse graph can be partit…

math.CO2025

Partition of Sparse Multigraphs into a Forest and a Forest with Restrictions

Ilkyoo Choi, Alexandr V. Kostochka, Matthew Yancey

The following measure of sparsity of multigraphs refining the maximum average degree: For $a > 0$ and an arbitrary real $b$ , a multigraph $H$ is \emph{ $(a, b)$ -sparse} if it is loople…

math.CO2024

Partition of Sparse Graphs into Two Forests with Bounded Degree

Matthew Yancey

Borodin and Kostochka proved that for $d_{2} \geq 2 d_{1} + 2$ and a graph $G$ where every subgraph $H$ satisfies $$ e(H) < \left(2 - \frac{d_2+2}{(d_1+2)(d_2+1)}\right)n(H) + \frac{1}{d_…

math.CO2020

Remarks on the Spectral Approach to Finding Short Paths

Kelly B Yancey, Matthew Yancey

We are interested in the general question: to what extent are the spectral properties of a graph connected to the distance function? Our motivation is a concrete example of this qu…

math.CO2020

Vertex Partitions into an Independent Set and a Forest with Each Component Small

Daniel W. Cranston, Matthew P. Yancey

For each integer k >= 2, we determine a sharp bound on mad(G) such that V(G) can be partitioned into sets I and F_k, where I is an independent set and G[F_k] is a forest in which e…

math.CO2019

Sparse graphs are near-bipartite

Daniel W. Cranston, Matthew P. Yancey

A multigraph $G$ is near-bipartite if $V (G)$ can be partitioned as $I, F$ such that $I$ is an independent set and $F$ induces a forest. We prove that a multigraph $G$ is near-bipart…