### A forcible version of Niessen's problem on degree sequences of graphs

*Jiyun Guo, Jianhua Yin*

#### Abstract

Let (a

_{1},a_{2},…,a_{n}) and (b_{1},b_{2},…,b_{n}) be two sequences of nonnegative integers satisfying the condition that b_{1}≥b_{2}≥⋯≥b_{n}, a_{i}≤ b_{i}for i=1,2,…,n and a_{i}+b_{i}≥a_{i+1}+b_{i+1}for i=1,2,…, n-1. In this paper, we give two different conditions, one of which is sufficient and the other one necessary, for the sequences (a_{1},a_{2},…,a_{n}) and (b_{1},b_{2},…,b_{n}) such that for every (c_{1},c_{2},…,c_{n}) with a_{i}≤c_{i}≤b_{i}for i=1,2,…,n and ∑&limits;_{i=1}^{n}c_{i}≡0 (mod 2), there exists a simple graph G with vertices v_{1},v_{2},…,v_{n}such that d_{G}(v_{i})=c_{i}for i=1,2,…,n. This is a variant of Niessen's problem on degree sequences of graphs (Discrete Math., 191 (1998), 247 13;253).Full Text: PDF PostScript