Making a C6-free graph C4-free and bipartite
نویسندگان
چکیده
Let e(G) denote the number of edges in a graph G, and let Ck denote a k-cycle. It is well-known that every graph has a bipartite subgraph with at least half as many edges. Győri showed that any bipartite, C6-free graph contains a C4-free subgraph containing at least half as many edges. Applying these two results in sequence we see that every C6-free graph, G, has a bipartite C4-free subgraph, H, with e(H) ≥ e(G)/4. We show that the factor of 1/4 can be improved to 3/8:
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 209 شماره
صفحات -
تاریخ انتشار 2016