Decompositions of graphs into cycles of length seven and single edges

Citation:
Sousa, Teresa. "Decompositions of graphs into cycles of length seven and single edges." Ars Combinatoria. 119 (2015): 321-329.

Abstract:

Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let f_H(n) be the smallest number t such that any graph G of order n admits an H-decomposition with at most t parts. Here we study the case when H=C_7, that is, the cycle of length 7 and prove that f_{C_7}(n)=\lfloor n^2/4 \rfloor for all n≥10.

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