Strong Circuit Double Cover of Some Cubic Graphs. Issue 2 (14th April 2014)

• Record Type: Journal Article
• Authors: Miao, Zhengke; Tang, Wenliang; Zhang, Cun‐Quan
• Is Part Of: Journal of graph theory. Volume 78:Issue 2(2015)
• Page Start: 131
• Page End: 142
• Publication Date: 2014-04-14
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21794
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Let <italic>C</italic> be a given circuit of a bridgeless cubic graph <italic>G</italic>. It was conjectured by Seymour that <italic>G</italic> has a circuit double cover (CDC) containing the given circuit <italic>C</italic>. This conjecture (strong CDC [SCDC] conjecture) has been verified by Fleischner and Häggkvist for various families of graphs and circuits. In this article, some of these earlier results have been improved: (1) if <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ntbz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21794:jgt21794-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo>−</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> contains a Hamilton path or a <italic>Y</italic>‐tree of order less than 14, then <italic>G</italic> has a CDC containing <italic>C</italic>; (2) if <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7nt9d" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21794:jgt21794-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mi>G</mml:mi><mml:mo>−</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> is connected and <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7nt8v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21794:jgt21794-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>|</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>H</mml:mi><mml:mo>)</mml:mo><mml:mo>|</mml:mo><mml:mo>≤</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>, then <italic>G</italic> has a CDC containing <italic>C</italic>.</p> </abstract>