Minimum K2, 3-Saturated Graphs

A graph is K2, 3‐saturated if it has no subgraph isomorphic to K2, 3, but does contain a K2, 3 after the addition of any new edge. We prove that the minimum number of edges in a K2, 3‐saturated graph on n≥5 vertices is sat(n,K2,3)=2n−3.

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Bibliographic Details
Published inJournal of graph theory Vol. 76; no. 4; pp. 309 - 322
Main Author Chen, Ya-Chen
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.08.2014
Wiley Subscription Services, Inc
Subjects
1991 Mathematics Subject Classification: 05C35
3-saturated graphs
extremal graphs
forbidden subgraphs
Graphs
K2, 3‐saturated graphs
Online AccessGet full text
ISSN0364-9024
1097-0118
DOI10.1002/jgt.21767

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Summary:A graph is K2, 3‐saturated if it has no subgraph isomorphic to K2, 3, but does contain a K2, 3 after the addition of any new edge. We prove that the minimum number of edges in a K2, 3‐saturated graph on n≥5 vertices is sat(n,K2,3)=2n−3.
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ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21767