Delay colourings of cubic graphs

TL;DR

This paper proves a specific case of a conjecture on delay colorings in bipartite multigraphs, showing that such graphs with delay 3 can be colored with 4 colors, and discusses related conjectures.

Contribution

It establishes the conjecture for bipartite multigraphs with delay 3, extending the understanding of delay colorings in graph theory.

Findings

Bipartite multigraphs with delay 3 can be edge-colored with 4 colors.

The proof confirms the conjecture for this specific case.

Connections to the Brualdi-Ryser-Stein conjecture are explored.

Abstract

In this note we prove the conjecture of \cite{HaWiWi} that every bipartite multigraph with integer edge delays admits an edge colouring with $d+1$ colours in the special case where $d=3$. A connection to the Brualdi-Ryser-Stein conjecture is discussed.