Solution to a Forcible Version of a Graphic Sequence Problem

Mao-cheng Cai; Liying Kang

paper

Solution to a Forcible Version of a Graphic Sequence Problem

arXiv:2110.04818

Abstract

Let $A_{n} = (a_{1}, a_{2}, \dots, a_{n})$ and $B_{n} = (b_{1}, b_{2}, \dots, b_{n})$ be nonnegative integer sequences with $A_{n} \leq B_{n}$ . The purpose of this note is to give a good characterization such that every integer sequence $π = (d_{1}, d_{2}, \dots d_{n})$ with even sum and $A_{n} \leq π \leq B_{n}$ is graphic. This solves a forcible version of problem posed by Niessen and generalizes the Erdős--Gallai theorem.