Even Subdivision-Factors of Cubic Graphs
arXiv:1211.1714
Abstract
We call a set of graphs an "even subdivison-factor" of a cubic graph if contains a spanning subgraph such that every component of has an even number of vertices and is a subdivision of an element of . We show that any set of 2-connected graphs which is an even subdivison-factor of every 3-connected cubic graph, satisfies certain properties. As a consequence, we disprove a conjecture which was stated in an attempt to solve the circuit double cover conjecture.