Incidence bounds on Edge Partitions of $K_n$

TL;DR

This paper establishes precise bounds on how edges of a complete graph can be partitioned, addressing a conjecture and exploring connections to graph connectivity and regularity.

Contribution

It provides the first sharp bounds for edge partitions in complete graphs, confirming the conjecture by Cheriyan and analyzing related graph properties.

Findings

Sharp bounds for edge partitions of $K_n$ are proven.

The bounds are shown to be optimal and cannot be improved.

Connections to node connectivity in strongly regular graphs are discussed.

Abstract

We solve a problem conjectured by Cheriyan, giving sharp bounds for incidence of certain edge partitions of the connected graph on $n$-vertices. We briefly discuss the history of the problem and relation to node connectivity of strongly regular graphs. We show that the bound cannot be made sharper.