Weak saturation numbers of K2 , t and K p ⋃ K q

Weak saturation numbers of K2 , t and K p ⋃ K q

A graph G is weakly F-saturated if G contains no copy of F, and there is an ordering of all edges of G¯so that if they are added one at a time, they form a complete graph and each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n is weak saturation numbe...

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Main Authors: Yajuan Cui, Liqun Pu
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860016301426
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spelling doaj-b4d13ab49ea14b9aa4700d069694c8872020-11-25T03:31:57ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163237240Weak saturation numbers of K2 , t and K p ⋃ K qYajuan Cui0Liqun Pu1The State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaSchool of Mathematics and Statistics of Zhengzhou University, Zhengzhou, 450001, China; Corresponding author.A graph G is weakly F-saturated if G contains no copy of F, and there is an ordering of all edges of G¯so that if they are added one at a time, they form a complete graph and each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n is weak saturation number, denoted by wsat(n,F). Let Ktdenote the complete graph with t vertices, Kp,qdenote the complete bipartite graph with partite sizes of p and q, and Kp⋃Kqdenote the complement of Kp,q. In this paper, we determine wsat(n,Kp⋃Kq)and wsat(n,K2,t)whose significance can be seen in the introduction. Keywords: Weakly saturated graph, Weak saturation number, Complete graph, Complete bipartite graphhttp://www.sciencedirect.com/science/article/pii/S0972860016301426
collection DOAJ
language English
format Article
sources DOAJ
author Yajuan Cui
Liqun Pu
spellingShingle Yajuan Cui
Liqun Pu
Weak saturation numbers of K2 , t and K p ⋃ K q
AKCE International Journal of Graphs and Combinatorics
author_facet Yajuan Cui
Liqun Pu
author_sort Yajuan Cui
title Weak saturation numbers of K2 , t and K p ⋃ K q
title_short Weak saturation numbers of K2 , t and K p ⋃ K q
title_full Weak saturation numbers of K2 , t and K p ⋃ K q
title_fullStr Weak saturation numbers of K2 , t and K p ⋃ K q
title_full_unstemmed Weak saturation numbers of K2 , t and K p ⋃ K q
title_sort weak saturation numbers of k2 , t and k p ⋃ k q
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2019-12-01
description A graph G is weakly F-saturated if G contains no copy of F, and there is an ordering of all edges of G¯so that if they are added one at a time, they form a complete graph and each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n is weak saturation number, denoted by wsat(n,F). Let Ktdenote the complete graph with t vertices, Kp,qdenote the complete bipartite graph with partite sizes of p and q, and Kp⋃Kqdenote the complement of Kp,q. In this paper, we determine wsat(n,Kp⋃Kq)and wsat(n,K2,t)whose significance can be seen in the introduction. Keywords: Weakly saturated graph, Weak saturation number, Complete graph, Complete bipartite graph
url http://www.sciencedirect.com/science/article/pii/S0972860016301426
work_keys_str_mv AT yajuancui weaksaturationnumbersofk2tandkpkq
AT liqunpu weaksaturationnumbersofk2tandkpkq
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