Alexander Clow

collaborators

10 papers

math.CO2026

MAD Phase Transitions in the Oriented Chromatic Number

Alexander Clow

For an oriented graph $G$ the oriented chromatic number of $G$ , written $I ¨ _{o} (G)$ , is the least integer $t$ such that $G$ has a homomorphism to a tournament on $t$ vertices. The or…

math.CO2026

Greedily Constructing Small Quasi-Kernels

Alexander Clow

In a digraph $D$ ,a quasi-kernel is an independent set $Q$ such that for every vertex $u$ , there is a vertex $v \in Q$ satisfying $dist (v, u) \leq 2$ . In 1974 ChvÃ¡tal and LovÃ…

math.CO2025

Improved Bounds for the Ultimate Independence Ratio of Odd Wheels

Alexander Clow, Hitesh Kumar, Shivaramakrishna Pragada

The ultimate independence ratio of a graph $G$ is defined as $I (G) = lim_{k \to \infty} \frac{I ^ \pm ( G ^{□ k} )}{∣ V ( G ) ∣ ^{k}},$ where $I^\pm (G^{□ k})$ is the independen…

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 $I^\pm_{d} (G)$ be the order of a largest induced $d$ -degenerate subgraph of $G$ . We prove that for any pair of non-negative integers…

math.CO2025

Cops and Robbers on Graphs with Path Constraints

Alexander Clow, Erin Meger

In 2019, Sivaraman conjectured that every $P_{k}$ -free graph has cop number at most $k - 3$ . In the same year, Liu proved this conjecture for $(P_{k}, claw)$ -free graphs. Recently…

math.CO2025

Tight Bounds for Cycle-Edge Decompositions and Covers

Saieed Akbari, Jonny Aloni, Arash Beikmohammadi +1

An old conjecture of Erd{Å}s and Gallai states that every $n$ vertex graph can be decomposed, that is $E (G)$ can be partitioned, into $O (n)$ cycles and edges. The covering version…