A constructive proof of the Fulkerson–Ryser characterization of digraphic sequences
-
Published:2023-06-30
Issue:
Volume:
Page:
-
ISSN:1793-8309
-
Container-title:Discrete Mathematics, Algorithms and Applications
-
language:en
-
Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Mukhopadhyay Asish1,
John Daniel1
Affiliation:
1. School of Computer Science, University of Windsor, Windsor, ON N9P 3W4, Canada
Abstract
Analogous to the Erdos–Gallai inequalities that give necessary and sufficient conditions for the existence of a graph on [Formula: see text] vertices with prescribed vertex degrees, the Ryser–Fulkerson inequalities give necessary and sufficient conditions for the existence of a digraph on [Formula: see text] vertices with prescribed indegrees and outdegrees of the vertices. In this note, we give a short constructive proof of the sufficiency of the Ryser–Fulkerson inequalities.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics