On restricted edge-colorings of bicliques
type: Item
instance of: scholarly article
title: On restricted edge-colorings of bicliques
zbMATH Open document ID: 1015.05059
DOI: 10.1016/S0012-365X(02)00510-1
author: Dhruv Mubayi
author: Douglas B. West
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: For graphs \(G\) and \(H\) and integers \(q \leq q'\), an \((H; q, q')\)-coloring of \(G\) is an edge coloring of \(G\) such that every copy of \(H\) in \(G\) receives at least \(q\) colors and at most \(q'\) colors. The maximum number and minimum number of colors in an \((H; q, q')\)-coloring of \(G\) is denoted by \(r(G, H: q, q')\) and \(R(G, H: q, q')\) respectively. The numbers \(r\) and \(R\) are investigated for complete bipartite graphs \(G\) and \(H\). For example, it is shown that \(R(K_{n,n}, K_{p,p}: q, p) = n\) for \(2 \leq p \leq n\) and \(1 \leq q \leq p\). Results on the numbers \(r\) and \(R\) are used to improve bounds on bipartite Turán numbers.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1839010
zbMATH Keywords: edge colorings
zbMATH Keywords: Turán numbers
zbMATH Keywords: bipartite graphs
reviewed by: Ralph Faudree
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839010