About The Second Neighborhood Problem in Tournaments Missing Disjoint Stars

TL;DR

This paper proves Seymour's Second Neighborhood Conjecture for tournaments missing disjoint star subgraphs under certain conditions, providing specific cases and examples where the conjecture holds.

Contribution

It establishes the conjecture for a new class of tournaments with missing disjoint stars and identifies conditions under which the property is guaranteed.

Findings

Proves the conjecture for tournaments missing disjoint stars.

Identifies weaker conditions for small cases n=2 or 3.

Provides examples of vertices satisfying the conjecture.

Abstract

We prove Seymour's Second Neighborhood Conjecture when the missing graph is disjoint stars under some conditions. Weaker conditions are required when n=2 or 3. In some cases, we exhibit two vertices with the desired property.