Edge-disjoint induced subgraphs with given minimum degree

Raphael Yuster

doi:10.37236/2882

Edge-disjoint induced subgraphs with given minimum degree

Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 > n^1+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
Journal	Electronic Journal of Combinatorics
Volume	20
Issue number	1
DOIs	https://doi.org/10.37236/2882
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

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10.37236/2882

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Edge-disjoint induced subgraphs with given minimum degree

Abstract

Keywords

ASJC Scopus subject areas

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