Michael C. Wigal

collaborators

8 papers

math.CO2025

Improving Uniquely Decodable Codes in Binary Adder Channels

JÃ³zsef Balogh, The Nguyen, Patric R. J. Ostergard +2

We present a general method to modify existing uniquely decodable codes in the $T$ -user binary adder channel. If at least one of the original constituent codes does not have averag…

math.CO2025

Packing edge disjoint cliques in graphs

JÃ³zsef Balogh, Michael C. Wigal

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

math.CO2025

Toward Vu's conjecture

Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku +1

In 2002, Vu conjectured that graphs of maximum degree $I^$ and maximum codegree at most $I^¶ I^$ have chromatic number at most $(I^¶ + o (1)) I^$ . Despite its importance, the conjecture h…

math.CO2025

TurÃ¡n 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.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

On Tutte cycles containing three prescribed edges

Michael C. Wigal, Xingxing Yu

A cycle $C$ in a graph $G$ is called a Tutte cycle if, after deleting $C$ from $G$ , each component has at most three neighbors on $C$ . Tutte cycles play an important role in the st…