Interval edge-colorings of K_{1,m,n}

TL;DR

This paper proves that the complete tripartite graph K_{1,m,n} can be edge-colored with intervals if and only if the greatest common divisor of m+1 and n+1 is 1, confirming a conjecture by Petrosyan.

Contribution

It establishes a precise condition for interval edge-colorability of K_{1,m,n}, settling a conjecture in graph theory.

Findings

K_{1,m,n} is interval edge-colorable iff gcd(m+1,n+1)=1

Confirmed Petrosyan's conjecture on this class of graphs

Provides a complete characterization for these graphs' colorability

Abstract

In this note we prove that K_{1,m,n} is interval edge-colorable if and only if gcd(m+1,n+1)=1. It settles in the affirmative a conjecture of Petrosyan.