ArticleOriginal scientific text
Title
Partitions of a graph into cycles containing a specified linear forest
Authors 1, 2
Affiliations
- Department of Mathematical Information Science, Tokyo University of Science, Tokyo 162-8601, Japan
- Kyoto Computer Gakuin, Kyoto 601-8407, Japan
Abstract
In this note, we consider the partition of a graph into cycles containing a specified linear forest. Minimum degree and degree sum conditions are given, which are best possible.
Keywords
partition of a graph, vertex-disjoint cycle, 2-factor, linear forest
Bibliography
- S. Brandt, G. Chen, R.J. Faudree, R.J. Gould and L. Lesniak, Degree conditions for 2-factors, J. Graph Theory 24 (1997) 165-173, doi: 10.1002/(SICI)1097-0118(199702)24:2<165::AID-JGT4>3.0.CO;2-O
- G. Chartrand and L. Lesniak, Graphs & Digraphs, 4th edition (Chapman & Hall, London, 2004).
- Y. Egawa, H. Enomoto, R.J. Faudree, H. Li and I. Schiermeyer, Two factors each component of which contains a specified vertex, J. Graph Theory 43 (2003) 188-198, doi: 10.1002/jgt.10113.
- Y. Egawa, R.J. Faudree, E. Györi, Y. Ishigami, R.H. Schelp and H. Wang, Vertex-disjoint cycles containing specified edges, Graphs Combin. 16 (2000) 81-92, doi: 10.1007/s003730050005.
- Y. Egawa and R. Matsubara, Vertex-disjoint cycles containing specified vertices in a graph, AKCE Int. J. Graphs Comb. 3 (1) (2006) 65-92.
- H. Enomoto, Graph partition problems into cycles and paths, Discrete Math. 233 (2001) 93-101, doi: 10.1016/S0012-365X(00)00229-6.
- H. Enomoto and H. Matsumura, Cycle-partition of a graph with specified vertices and edges, to appear in Ars Combinatoria.
- Y. Ishigami and H. Wang, An extension of a theorem on cycles containing specified independent edges, Discrete Math. 245 (2002) 127-137, doi: 10.1016/S0012-365X(01)00137-6.
- A. Kaneko and K. Yoshimoto, On a 2-factor with a specified edge in a graph satisfying the Ore condition, Discrete Math. 257 (2002) 445-461, doi: 10.1016/S0012-365X(02)00506-X.
- R. Matsubara and T. Sakai, Cycles and degenerate cycles through specified vertices, Far East J. Appl. Math. 20 (2005) 201-208.
- T. Sakai, Degree-sum conditions for graphs to have 2-factors with cycles through specified vertices, SUT J. Math. 38 (2002) 211-222.