Anti-Ramsey numbers in complete \(k\)-partite graphs
type: Item
instance of: scholarly article
title: Anti-Ramsey numbers in complete \(k\)-partite graphs
zbMATH Open document ID: 1459.05198
DOI: 10.1155/2020/5136104
author: Jili Ding
author: Hong Bian
author: Haizheng Yu
published in: Mathematical Problems in Engineering
publication date: 2020-10-13T00:00:00Z
review text: Summary: The anti-Ramsey number \(AR\left( G, H\right)\) is the maximum number of colors in an edge-coloring of \(G\) such that \(G\) contains no rainbow subgraphs isomorphic to \(H\). In this paper, we discuss the anti-Ramsey numbers \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{T}_n\right)\), \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{M}\right)\), and \(AR\left( K_{p_1, p_2, \ldots, p_k}, \mathcal{C}\right)\) of \(K_{p_1, p_2, \ldots, p_k} \), where \(\mathcal{T}_n\), \(\mathcal{M}\), and \(\mathcal{C}\) denote the family of all spanning trees, the family of all perfect matchings, and the family of all Hamilton cycles in \(K_{p_1, p_2, \ldots, p_k}\), respectively.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 7259943
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/5136104
OpenAlex ID: W3083432311
cites work: Q5422499
cites work: Q4075490
cites work: An anti-Ramsey theorem on cycles
cites work: Anti-Ramsey numbers for graphs with independent cycles
cites work: Edge-colorings with no large polychromatic stars
cites work: On the anti-Ramsey numbers for spanning trees
cites work: Complete solution for the rainbow numbers of matchings
cites work: The anti-Ramsey number of perfect matching
cites work: Bipartite rainbow numbers of matchings
cites work: Bipartite anti-Ramsey numbers of cycles
cites work: Q2931471
cites work: Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs
cites work: Rainbows in the hypercube
cites work: Rainbow numbers for matchings in plane triangulations
cites work: Planar anti-Ramsey numbers of paths and cycles
description: scientific article; zbMATH DE number 7259943