Abstract
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 ε> 0, if m > n1+ε, 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.
Original language | English |
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Journal | Electronic Journal of Combinatorics |
Volume | 20 |
Issue number | 1 |
DOIs | |
State | Published - 8 Mar 2013 |
Keywords
- Edge packing
- Induced subgraph
- Minimum degree subgraph
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics