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DISJOINT CYCLES WITH PRESCRIBED LENGTHS AND INDEPENDENT EDGES IN GRAPHS
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 Title & Authors
DISJOINT CYCLES WITH PRESCRIBED LENGTHS AND INDEPENDENT EDGES IN GRAPHS
Wang, Hong;
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 Abstract
We conjecture that if is an integer and G is a graph of order n with minimum degree at least (n+2k)/2, then for any k independent edges , , in G and for any integer partition with , G has k disjoint cycles , , of orders , , , respectively, such that passes through for all . We show that this conjecture is true for the case k = 2. The minimum degree condition is sharp in general.
 Keywords
cycles;disjoint cycles;cycle coverings;
 Language
English
 Cited by
 References
1.
S. Abbasi, Spanning cycles in dense graphs, Ph.D. thesis, Rutgers University, 1999.

2.
B. Bollobas, Extremal Graph Theory, Academic Press, London, 1978.

3.
J. Bondy and V. Chvatal, A method in graph theory, Discrete Math. 15 (1976), no. 2, 111-135. crossref(new window)

4.
Y. Egawa, R. Faudree, E. Gyori, Y. Ishigami, R. Schelp, and H. Wang, Vertex-disjoint cycles containing specified edges, Graphs Combin. 16 (2000), no. 1, 81-92. crossref(new window)

5.
M. H. El-Zahar, On circuits in graphs, Discrete Math. 50 (1984), no. 2-3, 227-230. crossref(new window)

6.
P. Erdos and T. Gallai, On maximal paths and circuits of graphs, Acta Math. Acad. Sci. Hungar 10 (1959), 337-356.

7.
C. Magnant and K. Ozeki, Partitioning graphs into paths and cycles, J. Comb. 3 (2012), no. 2, 135-161.

8.
H. Wang, Covering a graph with cycles passing through given edges, J. Graph Theory 26 (1997), no. 2, 105-109. crossref(new window)

9.
J. E.Williamson, Panconnected graph II, Period. Math. Hungar. 8 (1977), no. 2, 105-116. crossref(new window)