Tripartite Ramsey number r t(K 2,4, K 2,4)

A graph G is n - partite, n ≥ 1, if it is possible to partition the set of points V (G) into n subsets V 1 ,V 2 ,... V n (called partite sets) such that every element of the set of lines E(G) joins a point of V...

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Main Authors: Buada S., Longani V.
Format: Journal
Published: 2017
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84864125348&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/42858
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-428582017-09-28T06:41:08Z Tripartite Ramsey number r t(K 2,4, K 2,4) Buada S. Longani V. A graph G is n - partite, n ≥ 1, if it is possible to partition the set of points V (G) into n subsets V 1 ,V 2 ,... V n (called partite sets) such that every element of the set of lines E(G) joins a point of V i to a point of V j , i ≠ j. For n = 2, and n = 3 such graphs are called bipartite graph, and tripartite graph respectively. A complete n-partite graph G is an n-partite graph with the added property that if u ∈ V i and v ∈ V j , i ≠ j, then the line uv ∈ E(G). If |V i | = p i , then this graph is denoted by K p1,p2,...,pn . For the complete tripartite graph K s,s,s with the number of points p = 3s, let each line of the graph has either red or blue colour. The smallest number s such that K s,s,s always contains K m,n with all lines of K m,n have one colour (red or blue) is called tripartite Ramsey number and denoted by r t (K m,n , K m,n ). In this paper, we show that r t (K 2,4 , K 2,4 ) = 7. © 2012 by the Mathematical Association of Thailand. All rights reserved. 2017-09-28T06:41:08Z 2017-09-28T06:41:08Z 2012-04-01 Journal 16860209 2-s2.0-84864125348 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84864125348&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/42858
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
description A graph G is n - partite, n ≥ 1, if it is possible to partition the set of points V (G) into n subsets V 1 ,V 2 ,... V n (called partite sets) such that every element of the set of lines E(G) joins a point of V i to a point of V j , i ≠ j. For n = 2, and n = 3 such graphs are called bipartite graph, and tripartite graph respectively. A complete n-partite graph G is an n-partite graph with the added property that if u ∈ V i and v ∈ V j , i ≠ j, then the line uv ∈ E(G). If |V i | = p i , then this graph is denoted by K p1,p2,...,pn . For the complete tripartite graph K s,s,s with the number of points p = 3s, let each line of the graph has either red or blue colour. The smallest number s such that K s,s,s always contains K m,n with all lines of K m,n have one colour (red or blue) is called tripartite Ramsey number and denoted by r t (K m,n , K m,n ). In this paper, we show that r t (K 2,4 , K 2,4 ) = 7. © 2012 by the Mathematical Association of Thailand. All rights reserved.
format Journal
author Buada S.
Longani V.
spellingShingle Buada S.
Longani V.
Tripartite Ramsey number r t(K 2,4, K 2,4)
author_facet Buada S.
Longani V.
author_sort Buada S.
title Tripartite Ramsey number r t(K 2,4, K 2,4)
title_short Tripartite Ramsey number r t(K 2,4, K 2,4)
title_full Tripartite Ramsey number r t(K 2,4, K 2,4)
title_fullStr Tripartite Ramsey number r t(K 2,4, K 2,4)
title_full_unstemmed Tripartite Ramsey number r t(K 2,4, K 2,4)
title_sort tripartite ramsey number r t(k 2,4, k 2,4)
publishDate 2017
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84864125348&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/42858
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