Even Cycles and Even 2-Factors in the Line Graph of a Simple Graph
نویسندگان
چکیده
Let G be a connected graph with an even number of edges. We show that if the subgraph of G induced by the vertices of odd degree has a perfect matching, then the line graph of G has a 2-factor whose connected components are cycles of even length (an even 2-factor). For a cubic graph G, we also give a necessary and sufficient condition so that the corresponding line graph L(G) has an even cycle decomposition of index 3, i.e., the edge-set of L(G) can be partitioned into three 2-regular subgraphs whose connected components are cycles of even length. The more general problem of the existence of even cycle decompositions of index m in 2d-regular graphs is also addressed.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017