Sparse spanning κ-connected subgraphs in tournaments

Abstract

In 2009, Bang-Jensen asked whether there exists a function g(κ) such that every strongly κ-connected n-vertex tournament contains a strongly κ-connected spanning subgraph with at most κn + g(κ) arcs. In this paper, we answer the question by showing that every strongly kconnected n-vertex tournament contains a strongly κ-connected spanning subgraph with at most κn+750κ2 log2(κ+1) arcs, and there is a polynomial-time algorithm to find the spanning subgraph. © 2017 Society for Industrial and Applied Mathematics.