Decompositions of graphs into trees, forests, and regular subgraphs

A conjecture by A. Hoffmann-Ostenhof suggests that any connected cubic graph G contains a spanning tree T for which every component of G−E(T) is a K1, a K2, or a cycle. We show that any cubic graph G contains a spanning forest F for which every component of G−E(F) is a K2 or a cycle, and that any co...

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Bibliographic Details
Published inDiscrete mathematics Vol. 338; no. 8; pp. 1322 - 1327
Main Authors Akbari, Saieed, Jensen, Tommy R., Siggers, Mark
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.08.2015
Subjects
Graph factorization
Path-factorization
Spanning tree
Graph factorization
Path-factorization
Spanning tree
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Summary:A conjecture by A. Hoffmann-Ostenhof suggests that any connected cubic graph G contains a spanning tree T for which every component of G−E(T) is a K1, a K2, or a cycle. We show that any cubic graph G contains a spanning forest F for which every component of G−E(F) is a K2 or a cycle, and that any connected graph G≠K1 with maximal degree at most 3 contains a spanning forest F without isolated vertices for which every component of G−E(F) is a K1, a K2 or a cycle. We also prove a related statement about path-factorizations of graphs with maximal degree 3.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2015.02.021