Strongly even-cycle decomposable graphs
Tony Huynh, Andrew D. King, Sang-il Oum, Maryam Verdian-Rizi
TL;DR
This paper characterizes strongly even-cycle decomposable graphs, showing that certain composition operations preserve this property and providing an exact characterization for cographs.
Contribution
It introduces new preservation results for strongly even-cycle decomposability under graph composition operations and characterizes this property in cographs.
Findings
Composition operations preserving strongly even-cycle decomposability identified
Exact characterization of strongly even-cycle decomposable cographs provided
Theorems extend understanding of cycle decompositions in complex graphs
Abstract
A graph is strongly even-cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several fundamental composition operations that preserve the property of being Eulerian also yield strongly even-cycle decomposable graphs. As an easy application of our theorems, we give an exact characterization of the set of strongly even-cycle decomposable cographs.
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Taxonomy
Topicssemigroups and automata theory · Advanced Graph Theory Research · Rings, Modules, and Algebras