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Sparse Spanning $k$-Connected Subgraphs in Tournaments

Dong Yeap Kang, Jaehoon Kim, Younjin Kim, Geewon Suh
2017 SIAM Journal on Discrete Mathematics  

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2016 pre-print arXiv:1603.02474v1 fatcat:a5i2m6qgtzan3p7e4kq7jcil2y

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2018 accepted
arXiv:1603.02474v2 fatcat:ajxkhznvaffxppkeoea3tjmhte
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(k+1) arcs.
doi:10.1137/16m1064805 fatcat:ccu4bc6g4rfrzh4fr5556n6zc4
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Dong Yeap Kang, Jaehoon Kim, Younjin Kim, Geewon Suh. "Sparse Spanning $k$-Connected Subgraphs in Tournaments." SIAM Journal on Discrete Mathematics 31.3 (2017) 2206-2227