Aaron Abrams

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5 papers · 1 filter

math.CO2025

Evasive Random Walks and the Clairvoyant Demon

Aaron Abrams, Henry Landau, Zeph Landau +2

A pair of random walks $(R, S)$ on the vertices of a graph $G$ is {\it successful} if two tokens can be scheduled (moving only one token at a time) to travel along $R$ and $S$ witho…

math.CO2025

The $k^{t h}$ Upper Chromatic Number of the Line

Aaron Abrams

Let $S \subseteq R^{n}$ , and let $k \in N$ . Greenwell and Johnson define $I ¨^^{(k)} (S)$ to be the smallest integer $m$ (if such an integer exists) such that for…

math.CO2025

The number of possibilities for random dating

Aaron Abrams, Rod Canfield, Andrew Granville

Let $G$ be a regular graph and $H$ a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of $H$ one expects to find in a random subgraph…

math.CO2025

Yet Another Species of Forbidden-distances Chromatic Number

Aaron Abrams, Peter Johnson

This 2001 paper introduces a new type of chromatic number for point sets.

math.CO2025

Upper Chromatic Numbers: An Update

Aaron Abrams

This is a survey written in 2000 about upper chromatic numbers

Evasive Random Walks and the Clairvoyant Demon

The kth Upper Chromatic Number of the Line

The number of possibilities for random dating

Yet Another Species of Forbidden-distances Chromatic Number

Upper Chromatic Numbers: An Update

The $k^{t h}$ Upper Chromatic Number of the Line