Maximum even factors of graphs

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• 作者：Fuyuan Chen^a ; ^{chenfuyuan19871010@163.com" class="auth_mail" title="E-mail the corresponding author} ; Genghua Fan^b ; ¹ ; ^{fan@fzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Even graph ; Spanning subgraph ; Large even factor ; 2-Factor
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：119
• 期：Complete
• 页码：237-244
• 全文大小：268 K

文摘

A spanning subgraph F of a graph G is called an even factor of G if each vertex of F has even degree at least 2 in F. Kouider and Favaron proved that if a graph G has an even factor, then it has an even factor F   with d="mmlsi1" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0095895616000277&_mathId=si1.gif&_user=111111111&_pii=S0095895616000277&_rdoc=1&_issn=00958956&md5=0f3a57f27b5ab3312e784d350b3b4877">dth="172" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0095895616000277-si1.gif">dden">de">$|E(F)|\ge \frac{9}{16}(|E(G)|+1)$. In this paper we improve the coefficient d="mmlsi2" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0095895616000277&_mathId=si2.gif&_user=111111111&_pii=S0095895616000277&_rdoc=1&_issn=00958956&md5=30348217cfcddf333ef426d754416b30">dth="16" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0095895616000277-si2.gif">dden">de">$\frac{9}{16}$ to d="mmlsi3" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0095895616000277&_mathId=si3.gif&_user=111111111&_pii=S0095895616000277&_rdoc=1&_issn=00958956&md5=26c469c65fec1bfb857e50ff671268e4">dth="10" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0095895616000277-si3.gif">dden">de">$\frac{4}{7}$, which is best possible. Furthermore, we characterize all the extremal graphs, showing that if d="mmlsi24" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0095895616000277&_mathId=si24.gif&_user=111111111&_pii=S0095895616000277&_rdoc=1&_issn=00958956&md5=72fa52bc2fb8d89ec2009fc7d97d32f1">dth="168" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0095895616000277-si24.gif">dden">de">$|E(H)|\le \frac{4}{7}(|E(G)|+1)$ for every even factor H of G, then G belongs to a specified class of graphs.