(k,k-1)-双正则可图序列的公平划分

Judicious Balanced Bipartitions of (k,k-1)-Biregular Graphic Degree Sequence

摘要: 设π= （d₁,d₂,…,d_n）是非负整数序列，π₁,π₂是将π的所有元素划分为两部分后的两个子序列。如果-1≤|π₁|-| π₂|≤1，则称π₁ π₂ 是π的一个平衡二部划分，其中|π_i|(i=1,2)表示 π_i中的元素数目。设k和m是两个正整数，π= (k^m,(k-1)^m)是双正则可图序列。本文确定了 Ψ_max(π)的值和Ψ_min(π)的值。。

Abstract: Let π= （d₁,d₂,…,d_n be a graphic sequence of nonnegative integers and π₁,π₂ are two sequences that are obtained by partitioning the elements of π into two sets. A balanced bipartition of π is a bipartition π₁,π₂ such that -1≤|π₁|-| π₂|≤1, where |π_i|(i=1,2) is denoted to the number of elements of π_i. In this paper, let k and m be positive integers, we determine the values Ψ_max(π) and Ψ_min(π) of (k,k-1)-biregular graphic sequence π= (k^m,(k-1)^m).