Decomposing tournaments into paths
نویسندگان
چکیده
منابع مشابه
Decomposing oriented graphs into transitive tournaments
For an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is a tournament then f(G) < 5 21n (1 + o(1)) and there are tournaments for which f(G) > n/3000. For general G we prove that f(G) ≤ bn/3c and this is tight. Some related parameters are also considered. AMS classification ...
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It is known that the edge set of a 2-edge-connected 3-regular graph can be decomposed into paths of length 3. W. Li asked whether the edge set of every 2-edge-connected graph can be decomposed into paths of length at least 3. The graphs C3, C4, C5, and K4 − e have no such decompositions. We construct an infinite sequence {Fi}∞i=0 of nondecomposable graphs. On the other hand, we prove that every...
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متن کاملDisjoint paths in tournaments
Given k pairs of vertices (si, ti) (1 ≤ i ≤ k) of a digraph G, how can we test whether there exist k vertex-disjoint directed paths from si to ti for 1 ≤ i ≤ k? This is NP-complete in general digraphs, even for k = 2 [2], but for k = 2 there is a polynomial-time algorithm when G is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen [1]. Here we prove that...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2020
ISSN: 0024-6115,1460-244X
DOI: 10.1112/plms.12328