Decompositions of graphs into 5-cycles and other small graphs

Sousa, Teresa. "Decompositions of graphs into 5-cycles and other small graphs." Electronic Journal of Combinatorics. 12 (2005): R49, 7 pp.


If H is a family of graphs, then an H-decomposition of a graph G is a partition of the edges of G each element of which induces a copy of a graph in G.
This paper addresses the problem of finding the number φ(n,H), the smallest number k such that every graph on n vertices has an H-decomposition with at most k elements. φ(n,H) is found in the cases when H={K2,C5}; when H={K2,C5+e}, where e is a chord of the C5; when H={K2,K4−e}; and when H={K2,K3+e}, where e is a pendant edge added to one vertex in the K3.

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5-cycle.pdf91.31 KB