Graph Theory » Directed Graphs » Tournaments

Decomposing k-arc-strong tournament into k spanning strong digraphs ★★

Author(s): Bang-Jensen; Yeo

Conjecture   Every k-arc-strong tournament decomposes into k spanning strong digraphs.

Keywords:

Posted by fhavet
updated March 15th, 2013
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Graph Theory » Graph Algorithms

PTAS for feedback arc set in tournaments ★★

Author(s): Ailon; Alon

Question   Is there a polynomial time approximation scheme for the feedback arc set problem for the class of tournaments?

Keywords: feedback arc set; PTAS; tournament

Posted by fhavet
updated March 15th, 2013
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Graph Theory » Directed Graphs » Tournaments

Partitionning a tournament into k-strongly connected subtournaments. ★★

Author(s): Thomassen

Problem   Let $ k_1, \dots , k_p $ be positve integer Does there exists an integer $ g(k_1, \dots , k_p) $ such that every $ g(k_1, \dots , k_p) $-strong tournament $ T $ admits a partition $ (V_1\dots , V_p) $ of its vertex set such that the subtournament induced by $ V_i $ is a non-trivial $ k_i $-strong for all $ 1\leq i\leq p $.

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Posted by fhavet
updated March 15th, 2013
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