A Class of Three‐Colorable Triangle‐Free Graphs1. Issue 4 (19th March 2012)

• Record Type: Journal Article
• Authors: Radovanović, Marko; Vušković, Kristina
• Is Part Of: Journal of graph theory. Volume 72:Issue 4(2013)
• Page Start: 430
• Page End: 439
• Publication Date: 2012-03-19
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21651
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>The chromatic number of a triangle‐free graph can be arbitrarily large. In this article, we show that if all subdivisions of <italic>K</italic>_{2, 3} are also excluded as induced subgraphs, then the chromatic number becomes bounded by 3. We give a structural characterization of this class of graphs, from which we derive an <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1rzwpnj7" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:jgt21651:equation:jgt21651-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> coloring algorithm, where <italic>n</italic> denotes the number of vertices and <italic>m</italic> the number of edges of the input graph.</p> </abstract>