Jacobsthal Numbers in Generalized Petersen Graphs

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• 作者：Henning Bruhn ; Laura Gellert and Jacob G&uuml ; nther
• 刊名：Journal of Graph Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：84
• 期：2
• 页码：146-157
• 全文大小：401K
• ISSN：1097-0118

文摘

We prove that the number of 1-factorizations of a generalized Petersen graph of the type lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">GP(3k,k)l:math> is equal to the kth Jacobsthal number lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">J(k)l:math> when k is odd, and equal to lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">4J(k)l:math> when k is even. Moreover, we verify the list coloring conjecture for lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">GP(3k,k)l:math>.