Turán numbers of vertex-disjoint cliques in \(r\)-partite graphs

For two graphs \(G\) and \(H\), the Tur\'{a}n number \(ex(G,H)\) is the maximum number of edges in a subgraph of \(G\) that contains no copy of \(H\). Chen, Li, and Tu determined the Tur\'{a}n numbers \(ex(K_{m,n},kK_2)\) for all \(k\geq 1\) [7]. In this paper we will determine the Tur\�...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-09
Main Authors: De Silva, Jessica, Heysse, Kristin, Kapilow, Adam, Schenfisch, Anna, Young, Michael
Format: Article
Language:English
Subjects:
Graph theory
Graphs
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For two graphs \(G\) and \(H\), the Tur\'{a}n number \(ex(G,H)\) is the maximum number of edges in a subgraph of \(G\) that contains no copy of \(H\). Chen, Li, and Tu determined the Tur\'{a}n numbers \(ex(K_{m,n},kK_2)\) for all \(k\geq 1\) [7]. In this paper we will determine the Tur\'{a}n numbers \(ex(K_{a_1,\ldots,a_r},kK_r)\) for all \(r\geq 3\) and \(k\geq 1\).
ISSN:2331-8422