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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Bibliographic Details
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
Description
Summary: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
ISSN:0972-8600