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arXiv · 1603.02474

Sparse spanning $k$-connected subgraphs in tournaments

Dong Yeap Kang·Jaehoon Kim·Younjin Kim·Geewon Suh
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Abstract

In 2009, Bang-Jensen asked whether there exists a function $g(k)$ such that every strongly $k$-connected $n$-vertex tournament contains a strongly $k$-connected spanning subgraph with at most $kn + g(k)$ arcs. In this paper, we answer the question by showing that every strongly $k$-connected $n$-vertex tournament contains a strongly $k$-connected spanning subgraph with at most $kn + 750k^2\log(k+1)$ arcs.

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Dong Yeap Kang, Jaehoon Kim, Younjin Kim, Geewon Suh. 2018-01-22. Sparse spanning $k$-connected subgraphs in tournaments. https://doi.org/10.1137/16m1064805

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