{"title":"顶点可分解图的一种新构造","authors":"N. Hajisharifi, A. Tehranian","doi":"10.22108/TOC.2016.13316","DOIUrl":null,"url":null,"abstract":"Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x in V(G)$. The graph $Gcup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $Gsetminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G cup W(S)$ is a vertex decomposable graph.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"5 1","pages":"33-38"},"PeriodicalIF":0.6000,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A NEW CONSTRUCTION FOR VERTEX DECOMPOSABLE GRAPHS\",\"authors\":\"N. Hajisharifi, A. Tehranian\",\"doi\":\"10.22108/TOC.2016.13316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x in V(G)$. The graph $Gcup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $Gsetminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G cup W(S)$ is a vertex decomposable graph.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"5 1\",\"pages\":\"33-38\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2016-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2016.13316\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2016.13316","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设$G$是顶点集$V(G)$上的一个有限简单图，设$S subseteq V(G)$。在$x$处向$G$添加须意味着在$G$中添加一个新的顶点$y$和边缘$xy$，其中$x在V(G)$中。图$Gcup W(S)$由$G$通过在$S$的每个顶点上添加晶须而得到。证明了如果$ gset- S$是一个除了$3$或$5$以外没有无弦循环长度的图，有弦图或$C_5$，则$G cup W(S)$是一个顶点可分解图。
Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x in V(G)$. The graph $Gcup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $Gsetminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G cup W(S)$ is a vertex decomposable graph.
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