Edge-Disjoint Induced Subgraphs with Given Minimum Degree
نویسنده
چکیده
Let h be a given positive integer. For a graph with n vertices and m edges, what is the maximum number of pairwise edge-disjoint induced subgraphs, each having minimum degree at least h? There are examples for which this number is O(m2/n2). We prove that this bound is achievable for all graphs with polynomially many edges. For all > 0, if m > n1+ , then there are always Ω(m2/n2) pairwise edge-disjoint induced subgraphs, each having minimum degree at least h. Furthermore, any two subgraphs intersect in an independent set of size at most 1 + O(n3/m2), which is shown to be asymptotically optimal.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013