Work

Disjoint induced subgraphs of the same order and size

Year: 2013

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1312.1680

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

Institutions: London Institute for Mathematical Sciences, University of Memphis, University of Cambridge, University of Oxford

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Microsoft Research

Award: Random Geometric Graphs