Contractions, cycle double covers, and cyclic colorings in locally connected graphs

Authors:
Matthias Kriesell
Affiliations:
Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

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Abstract

A finite, undirected graph is called locally connected, if the neighborhood of every vertex induces a connected subgraph. In this paper we study the existence of edges in locally connected k-connected graphs whose contraction keeps the graph locally connected k-connected. As an application, we prove that the statement of the famous cycle double cover conjecture is true for locally connected graphs. Moreover, we prove that a conjecture of Plummer and Toft on cyclic colorings of 3-connected planar graphs holds when restricted to locally connected graphs.