Triply Existentially Complete Triangle‐Free Graphs. Issue 4 (27th May 2014)

• Record Type: Journal Article
• Authors: Even‐Zohar, Chaim; Linial, Nati
• Is Part Of: Journal of graph theory. Volume 78:Issue 4(2015)
• Page Start: 305
• Page End: 317
• Publication Date: 2014-05-27
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21808
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>A triangle‐free graph <italic>G</italic> is called <italic>k‐existentially complete</italic> if for every induced <italic>k</italic>‐vertex subgraph <italic>H</italic> of <italic>G</italic>, every extension of <italic>H</italic> to a <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf86362w" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21808:jgt21808-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>‐vertex triangle‐free graph can be realized by adding another vertex of <italic>G</italic> to <italic>H</italic>. Cherlin <xref ref-type="link" rid="jgt21808-bib-0011">11</xref><xref ref-type="link" rid="jgt21808-bib-0012">12</xref> asked whether <italic>k</italic>‐existentially complete triangle‐free graphs exist for every <italic>k</italic>. Here, we present known and new constructions of 3‐existentially complete triangle‐free graphs.</p> </abstract>