Triangle-free Uniquely 3-Edge Colorable Cubic Graphs
Sarah-Marie Belcastro, Ruth Haas
TL;DR
This paper introduces infinitely many new triangle-free cubic graphs that are uniquely 3-edge colorable, expanding the limited known examples from Tutte's 1976 graph.
Contribution
It provides the first infinite family of such graphs, significantly advancing understanding of uniquely 3-edge colorable cubic graphs.
Findings
Discovered infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs.
Extended the known class of such graphs beyond Tutte's single example.
Demonstrated structural properties enabling infinite constructions.
Abstract
This paper presents infinitely many new examples of triangle-free uniquely 3-edge colorable cubic graphs. The only such graph previously known was given by Tutte in 1976.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems