Strong chromatic index of subcubic planar multigraphs

TL;DR

This paper proves that every planar multigraph with maximum degree 3 has a strong chromatic index of at most 9, confirming a conjecture and establishing a precise bound for such graphs.

Contribution

It verifies a conjecture by Faudree et al. that the strong chromatic index of subcubic planar multigraphs is at most 9, which is proven to be sharp.

Findings

Confirmed the conjecture for subcubic planar multigraphs

Established the exact upper bound of 9 for the strong chromatic index

Demonstrated the bound is tight with examples

Abstract

The strong chromatic index of a multigraph is the minimum $k$ such that the edge set can be $k$-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gy\'{a}rf\'{a}s, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.