On Linial's Conjecture for Spine Digraphs

TL;DR

This paper introduces spine digraphs, a new class of digraphs with specific structural properties, and proves that Linial's Conjecture is valid for this class, expanding the understanding of the conjecture's scope.

Contribution

The paper defines spine digraphs and demonstrates that Linial's Conjecture holds for this new class, extending previous results to a broader family of digraphs.

Findings

Linial's Conjecture verified for spine digraphs

Spine digraphs generalize split digraphs

Structural properties facilitate proof of conjecture

Abstract

In this paper we introduce a superclass of split digraphs, which we call spine digraphs. Those are the digraphs D whose vertex set can be partitioned into two sets X and Y such that the subdigraph induced by X is traceable and Y is a stable set. We also show that Linial's Conjecture holds for spine digraphs.