Disjoint induced subgraphs of the same order and size

Béla Bollobás; Teeradej Kittipassorn; Bhargav Narayanan; Alex Scott

Disjoint induced subgraphs of the same order and size

Combinatorics 2016-09-07 v2

Authors: Béla Bollobás , Teeradej Kittipassorn , Bhargav Narayanan , Alex Scott

Abstract

For a graph $G$ , let $f(G)$ be the largest integer $k$ for which there exist two vertex-disjoint induced subgraphs of $G$ each on $k$ vertices, both inducing the same number of edges. We prove that $f(G) \ge n/2 - o(n)$ for every graph $G$ on $n$ vertices. This answers a question of Caro and Yuster.

Keywords

induced subgraphs vertex-disjoint graph theory extremal graph theory Caro-Yuster problem

Cite

@article{arxiv.1312.1680,
  title  = {Disjoint induced subgraphs of the same order and size},
  author = {Béla Bollobás and Teeradej Kittipassorn and Bhargav Narayanan and Alex Scott},
  journal= {arXiv preprint arXiv:1312.1680},
  year   = {2016}
}

Comments

25 pages, improved presentation, fixed misprints, European Journal of Combinatorics

Disjoint induced subgraphs of the same order and size

Abstract

Keywords

Cite

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