数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2009年
1期
36-39
,共4页
Ramsey数%连通图%悬挂树%色数
Ramsey數%連通圖%懸掛樹%色數
Ramsey수%련통도%현괘수%색수
Ramsey numbers%connected graph%pendent tree%chromatic number
设H是阶为n的连通图.在H的某一个顶点上悬挂一棵阶为 j 的树,得到图Hj,用Hj 表示这样的图形族.本文证明:当 j 充分大时,有r(G,Hj)=(X(G)-1)(n+j-1)+s(G),其中x(G),s(G)分别表示图G的色数和色数剩余.
設H是階為n的連通圖.在H的某一箇頂點上懸掛一棵階為 j 的樹,得到圖Hj,用Hj 錶示這樣的圖形族.本文證明:噹 j 充分大時,有r(G,Hj)=(X(G)-1)(n+j-1)+s(G),其中x(G),s(G)分彆錶示圖G的色數和色數剩餘.
설H시계위n적련통도.재H적모일개정점상현괘일과계위 j 적수,득도도Hj,용Hj 표시저양적도형족.본문증명:당 j 충분대시,유r(G,Hj)=(X(G)-1)(n+j-1)+s(G),기중x(G),s(G)분별표시도G적색수화색수잉여.
It gives the following Ramsey goodness conclusion. Let H be any connected graph of order n and let Hj be a graph of order n+j which is obtained from H by adding a pendent tree with j vertices, let Hj denote the class of all graphs Hj, if j is large enough, the Ramsey number r(G,Hj) satisfies r(G,Hj)=(X-1)(n+j-1)+s.
