| 摘要: |
| 考虑经典Turán型问题的变形:确定最小的正偶数σ(Kr,s-ke,n),s ≥ r ≥ k ≥ 1,使得对于每一个n项可图序列π=(d1,d2,…,dn),当σ(π)=d1+d2+…+dn ≥ σ(Kr,s-ke,n)时,π是蕴含几乎完全二部图Kr,s-ke可图的,即Kr,s-ke是从完全二部图Kr,s中删去k条边后所得的图,而这k条边构成Kr,s的一匹配.然后确定出当r=3,s ≥ 4且n充分大时,σ(Kr,s-ke,n)的值. |
| 关键词: 图 度序列 蕴含 几乎完全二部图 |
| DOI： |
| 投稿时间：2015-12-08 |
| 基金项目:宁夏大学青年教师科研启动项目(编号:QN0505);宁夏大学数学计算机学院青年教师科研启动基金项目联合资助 |
|
| Potentially K3, s-ke Graphical Sequences |
|
CHEN Gang
|
| (Department of Mathematics and Computer, Ningxia University, Yinchuan, Ningxia, 750021, China) |
| Abstract: |
| In this paper, we consider a variation of the classical Turán-type extremal problems as follows:determine the smallest positive even number σ (Kr, s-ke, n), s ≥ r ≥ k ≥ 1, such that every n term graphic sequence π= (d1, d2, …, dn) with term sum σ (π)=d1+d2+…+dn ≥ σ (Kr, s-ke, n) is potentially Kr, s-ke-graphic, where Kr, s-ke is an almost complete bipartite graph that obtained from a complete bipartite graph Kr, s by deleting k edges forming a matching.We determine the values of σ (Kr, s-ke, n) for r=3, s ≥ 4 and sufficiently large n. |
| Key words: graph degree sequence potentially almost complete bipartite graph |
