可图序列偏序集的极小元(英文)

Minimal Elements in the Poset of Graphic Sequences

英文关键词:graph  graphic sequence  poset  minimal elements.

中文摘要:

      ｎ项非增非负整数序列是可图的，若是某个阶简单图的度序列．所有项和为２ｍ、迹为ｆ的ｎ项可图序列的集合Ｇ_{ｎ，ｍ，ｆ}在优超关系下是一个偏序集．本文刻划了偏序集Ｇ_{ｎ，ｍ，ｆ}的极小元，并确定各种可图序列偏序集中极小元的个数．

英文摘要:

      A nonincreasing sequence ( of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n. The set of all graphic sequences of n terms with even sum 2m and trace f is a poset G_{ｎ，ｍ，ｆ} under majorization relation. The paper characterizes the minimal elements in the poset G_{ｎ，ｍ，ｆ} and determines the number of minimal elements in various posets of graphic sequences.