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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1394, author = {Ryota Matsubara and Hajime Matsumura}, title = {Partitions of a graph into cycles containing a specified linear forest}, journal = {Discussiones Mathematicae Graph Theory}, volume = {28}, year = {2008}, pages = {97-107}, zbl = {1170.05039}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1394} }
Ryota Matsubara; Hajime Matsumura. Partitions of a graph into cycles containing a specified linear forest. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 97-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1394/
[000] [1] 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 | Zbl 0879.05060
[001] [2] G. Chartrand and L. Lesniak, Graphs & Digraphs, 4th edition (Chapman & Hall, London, 2004).
[002] [3] 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. | Zbl 1024.05073
[003] [4] 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. | Zbl 0951.05061
[004] [5] Y. Egawa and R. Matsubara, Vertex-disjoint cycles containing specified vertices in a graph, AKCE Int. J. Graphs Comb. 3 (1) (2006) 65-92. | Zbl 1143.05044
[005] [6] H. Enomoto, Graph partition problems into cycles and paths, Discrete Math. 233 (2001) 93-101, doi: 10.1016/S0012-365X(00)00229-6. | Zbl 0985.05036
[006] [7] H. Enomoto and H. Matsumura, Cycle-partition of a graph with specified vertices and edges, to appear in Ars Combinatoria. | Zbl 1224.05403
[007] [8] 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. | Zbl 0990.05081
[008] [9] 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. | Zbl 1008.05118
[009] [10] R. Matsubara and T. Sakai, Cycles and degenerate cycles through specified vertices, Far East J. Appl. Math. 20 (2005) 201-208. | Zbl 1084.05038
[010] [11] T. Sakai, Degree-sum conditions for graphs to have 2-factors with cycles through specified vertices, SUT J. Math. 38 (2002) 211-222. | Zbl 1029.05127