Bounding the Feedback Vertex Number of Digraphs in Terms of Vertex Degrees

TL;DR

This paper generalizes classical bounds like Turan and Caro-Wei inequalities to directed graphs, providing new bounds on the feedback vertex number based on vertex degrees.

Contribution

It introduces novel bounds on the feedback vertex number of digraphs using outdegree and average outdegree, extending classical undirected graph results.

Findings

Derived bounds on feedback vertex number in terms of outdegrees

Extended Turan and Caro-Wei inequalities to directed graphs

Provided theoretical bounds applicable to digraph analysis

Abstract

The Turan bound is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality, which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We show how these statements can be generalized to directed graphs, thus yielding a bound on directed feedback vertex number in terms of vertex outdegrees and in terms of average outdegree, respectively.