A Characterization of Graphs with No Octahedron Minor. Issue 2 (26th September 2012)

• Record Type: Journal Article
• Authors: Ding, Guoli
• Is Part Of: Journal of graph theory. Volume 74:Issue 2(2013)
• Page Start: 143
• Page End: 162
• Publication Date: 2012-09-26
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21699
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>It is proved that a graph does not contain an octahedron minor if and only if it is constructed from <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg37c26b3v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21699:jgt21699-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mo>}</mml:mo></mml:mrow><mml:mo>∪</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:msubsup><mml:mi>C</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>:</mml:mo><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn>3</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math></alternatives> and five other internally 4‐connected graphs by 0‐, 1‐, 2‐, and 3‐sums.</p> </abstract>