Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

AN EXTREMAL PROBLEM ON POTENTIALLY $K_{r,r}$-ke-GRAPHIC SEQUENCES

  • Chen, Gang (Department of Mathematics, Ningxia University) ;
  • Yin, Jian-Hua (Department of Mathematics, College of Information Science and Technology, Hainan University)
  • 발행 : 2009.01.31
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초록

For $1{\leq}k{\leq}r$, let ${\sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${\pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${\sigma}({\pi})$ = $d_1$ + $d_2$ + ${\cdots}$ + $d_n\;{\geq}\;{\sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r\;{\times}\;r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${\sigma}$($K_{r,r}$ - ke, n) for even $r\;({\geq}4)$ and $n{\geq}7r^2+{\frac{1}{2}}r-22$ and for odd r (${\geq}5$) and $n{\geq}7r^2+9r-26$.

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