Answers to some problems about graph coloring test graphs
Takahiro Matsushita

TL;DR
This paper investigates properties of graph coloring test graphs, proving certain graphs are homotopy test graphs and exploring conditions under which graphs are Stiefel-Whitney test graphs, addressing open problems in the field.
Contribution
It proves that graphs with chromatic number 2 are homotopy test graphs and constructs a graph with two involutions where only one yields a Stiefel-Whitney test graph.
Findings
Graphs with chromatic number 2 are homotopy test graphs
Existence of a graph with two involutions where only one is a Stiefel-Whitney test graph
Answers to open problems posed by Kozlov
Abstract
We prove that a graph whose chromatic number is 2 is a homotopy test graph. We also prove that there is a graph with two involutions and such that is a Stiefel-Whitney test graph, but is not. These are answers to some of the problems suggested by Kozlov.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
