Michael C. Wigal

activity

20172025

most citedLarge cycles in essentially 4-connected graphs

1 citations · 1 across the 15 of their papers we have counts for

collaborators

17 papers

math.CO2025

Toward Vu's conjecture

Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku +1

In 2002, Vu conjectured that graphs of maximum degree $Δ$ and maximum codegree at most $ζ Δ$ have chromatic number at most $(ζ + o (1)) Δ$ . Despite its importance, the conjecture has re…

math.CO2025

Turán densities for matroid basis hypergraphs

Jorn van der Pol, Zach Walsh, Michael C. Wigal

Let $U$ be a uniform matroid. For all positive integers $n$ and $r$ with $n \geq r$ , what is the maximum number of bases of an $n$ -element, rank- $r$ matroid without $U$ as a minor?…

math.CO2025

Packing edge disjoint cliques in graphs

József Balogh, Michael C. Wigal

Let $r \geq 3$ be fixed and $G$ be an $n$ -vertex graph. A long-standing conjecture of Győri states that if $e (G) = t_{r - 1} (n) + k$ , where $t_{r - 1} (n)$ denotes the number of edges of…

math.CO2024

Longest Path and Cycle Transversals in Chordal Graphs

James A. Long, Kevin G. Milans, Michael C. Wigal

We show that if $G$ is a $n$ -vertex connected chordal graph, then it admits a longest path transversal of size $O (lo g^{2} n)$ . Under the stronger assumption of 2-connectivity, we sh…

math.CO2024

Clique covers and decompositions of cliques of graphs

József Balogh, Jialin He, Robert A. Krueger +2

In 1966, Erdős, Goodman, and Pósa showed that if $G$ is an $n$ -vertex graph, then at most $⌊ n^{2} /4 ⌋$ cliques of $G$ are needed to cover the edges of $G$ , and the bound…

math.CO2024

On the number of $P$ -free set systems for tree posets $P$

József Balogh, Ramon I. Garcia, Michael C. Wigal

We say a finite poset $P$ is a tree poset if its Hasse diagram is a tree. Let $k$ be the length of the largest chain contained in $P$ . We show that when $P$ is a fixed tree poset,…

Toward Vu's conjecture

Turán densities for matroid basis hypergraphs

Packing edge disjoint cliques in graphs

Longest Path and Cycle Transversals in Chordal Graphs

Clique covers and decompositions of cliques of graphs

On the number of P-free set systems for tree posets P

On the number of $P$ -free set systems for tree posets $P$