Elsevier

Discrete Applied Mathematics

Volume 159, Issue 17, 28 October 2011, Pages 2170-2174
Discrete Applied Mathematics

Note
Constructive extensions of two results on graphic sequences

https://doi.org/10.1016/j.dam.2011.06.017Get rights and content
Under an Elsevier user license
open archive

Abstract

A list of nonnegative integers is graphic if it is the list of vertex degrees of a graph. Erdős–Gallai characterized graphic lists, and Gale and Ryser, independently, provided one for a bipartite graph, given two lists of nonnegative integers. We give a constructive proof of an extension of these two results.

Highlights

► We provide constructive proofs of two theorems on graphic lists. ► The first construction deals with an extension of the Erdős–Gallai theorem. ► The second construction deals with the theorem of Gale and Ryser. ► Both constructions are based on a recent constructive proof of the first result.

Keywords

Graphic
Bigraphic
Realization
Lexicographic ordering
Good order

Cited by (0)