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111.
Romeo Rizzi 《Discrete Mathematics》2006,306(12):1177-1188
Given a digraph D=(V,A) and an X⊆V, DX denotes the digraph obtained from D by reversing those arcs with exactly one end in X. A digraph D is called acyclically pushable when there exists an X⊆V such that DX is acyclic. Huang, MacGillivray and Yeo have recently characterized, in terms of two excluded induced subgraphs on 7 and 8 nodes, those bipartite permutation digraphs which are acyclically pushable. We give an algorithmic proof of their result. Our proof delivers an O(m2) time algorithm to decide whether a bipartite permutation digraph is acyclically pushable and, if yes, to find a set X such that DX is acyclic. (Huang, MacGillivray and Yeo's result clearly implies an O(n8) time algorithm to decide but the polynomiality of constructing X was still open.)We define a strongly acyclic digraph as a digraph D such that DX is acyclic for every X. We show how a result of Conforti et al [Balanced cycles and holes in bipartite graphs, Discrete Math. 199 (1-3) (1999) 27-33] can be essentially regarded as a characterization of strongly acyclic digraphs and also provides linear time algorithms to find a strongly acyclic orientation of an undirected graph, if one exists. Besides revealing this connection, we add simplicity to the structural and algorithmic results first given in Conforti et al [Balanced cycles and holes in bipartite graphs, Discrete Math. 199 (1-3) (1999) 27-33]. In particular, we avoid decomposing the graph into triconnected components.We give an alternate proof of a theorem of Huang, MacGillivray and Wood characterizing acyclically pushable bipartite tournaments. Our proof leads to a linear time algorithm which, given a bipartite tournament as input, either returns a set X such that DX is acyclic or a proof that D is not acyclically pushable. 相似文献
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We call the tournament T an m-coloured tournament if the arcs of T are coloured with m-colours. If v is a vertex of an m-coloured tournament T, we denote by ξ(v) the set of colours assigned to the arcs with v as an endpoint.
In this paper is proved that if T is an m-coloured tournament with |ξ(v)|≤2 for each vertex v of T, and T satisfies at least one of the two following properties (1) m≠3 or (2) m=3 and T contains no C3 (the directed cycle of length 3 whose arcs are coloured with three distinct colours). Then there is a vertex v of T such that for every other vertex x of T, there is a monochromatic directed path from x to v.
Received: April, 2003 相似文献
115.
Sukhamay Kundu 《BIT Numerical Mathematics》1980,20(4):522-524
If each negative length arc of a digraphG is acyclic, i.e., does not belong to any cycle, then we show that the shortest paths from a given node to all other nodes can be computed inO(V
2) time, whereV is the number of nodes inG. 相似文献
116.
设D为有向图,T(D)为D的全有向图(Total-digraph),k(D)和p(D)分别为D的幂敛指数(Index of convergence)与周期(Period),本文证明了。1,对任意非平凡有向图D,p(T(D))=1,k(T(D))≤max{2p(D)-1,2K(D) 1},特别地,当D为本原有向图时,k(T(D))≤k(D) 1,当D不含有向圈时,k(T(D))=2k(D)-1;当D为有向圈Cn时,k(T(D))=2n-1.2。对任意非平凡强连通图D,k(T(D))≥Diam(D) 1。我们还证明了以上界是不可改进的最好界。 相似文献
117.
本文研究一类本原有向图的广义重下指数集 ,证明了 n(≥ 3)阶围长为 2的本原有向图的广义 k(≥ 2 )重下指数的最大值为 n-k,并给出其指数集的完全刻划 . 相似文献
118.
有向圈的行列式算法及HAMILTON图条件 总被引:6,自引:1,他引:5
本文引入有向路乘法、弧行列式等概念 ,讨论了弧行列式的性质 ,阐述了二种计算有向圈的行列式方法及有向图 D为 Hamilton图的充要条件 ,最后给出了计算实例 相似文献
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We study the class of 1‐perfectly orientable graphs, that is, graphs having an orientation in which every out‐neighborhood induces a tournament. 1‐perfectly orientable graphs form a common generalization of chordal graphs and circular arc graphs. Even though they can be recognized in polynomial time, little is known about their structure. In this article, we develop several results on 1‐perfectly orientable graphs. In particular, we (i) give a characterization of 1‐perfectly orientable graphs in terms of edge clique covers, (ii) identify several graph transformations preserving the class of 1‐perfectly orientable graphs, (iii) exhibit an infinite family of minimal forbidden induced minors for the class of 1‐perfectly orientable graphs, and (iv) characterize the class of 1‐perfectly orientable graphs within the classes of cographs and of cobipartite graphs. The class of 1‐perfectly orientable cobipartite graphs coincides with the class of cobipartite circular arc graphs. 相似文献