%0 Journal Article
%T <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <msub>   <mi>K</mi>   <mrow>    <mn>1</mn><mo>,</mo><mn>3</mn></mrow>  </msub>  </mrow></math>-Free图上的弦泛圈性<br>Chorded Pancyclicity on <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <msub>   <mi>K</mi>   <mrow>    <mn>1</mn><mo>,</mo><mn>3</mn></mrow>  </msub>  </mrow></math>-Free Graph
%A 李欢
%A 田增娴
%A 杨卫华
%J Advances in Applied Mathematics
%P 1994-1999
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.135187
%X 一个非诱导圈被称为弦圈，即在图中至少有一条额外的边连接圈内两个非相邻的顶点。一个阶数为<i>n</i>的图<i>G</i>, 如果<i>G</i>包含长度为从4到<i>n</i>的弦圈，则称为弦泛圈图。1991年，R.J. Faudree, R.J. Gould和T.E. Lindquester得出结论：令<i>G</i>是阶数为n(n≥14)的2-连通，K1,3-free图。如果对于每一对不相邻的顶点x,y，有|N(x)∪N(y)|≥2n？23，则<i>G</i>是泛圈图。在本文中，我们扩展了这个结果，把泛圈性推广到弦泛圈性：对于任意2-连通，阶数为n(n≥34)的K1,3-free图<i>G</i>，如果每对不相邻顶点x,y∈V(G)，满足|N(x)∪N(y)|≥2n？23，则图<i>G</i>是弦泛圈图。<br />
A non-induced cycle is called a chorded cycle, that is, a cycle that has at least one additional edge connecting two non-consecutive vertices within the cycle. A graph<i> G</i> of order<i> n</i> is chorded pancyclic if<i> G</i> contains a chorded cycle of each length from 4 to <i>n</i>. In 1991, R.J. Faudree, R.J. Gould, and T.E. Lindquester concluded: Let<i> G</i> be a 2-connectedK1,3-free graph with the ordern(n≥14). If|N(x)∪N(y)|≥2n？23for each pair of nonadjacent verticesx,y, then<i> G</i> is pancyclic. In this paper, we extended this result by generalizing the concept of pancyclicto chorded pancyclic: ever 2-connected,K1,3-free graph <i>G</i> with ordern≥43is chorded pancyclic if the number of the union of for each pair of nonadjacent vertices at least2n？23.
%K -Free，弦圈，泛圈，弦泛圈，哈密尔顿<br>-Free
%K Chorded Cycle
%K Pancyclic
%K Chorded Pancyclic
%K Hamiltonian
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=87252