The $1$-factors of oriented graphs
نویسندگان
چکیده
منابع مشابه
The 1-factors of Oriented Graphs
1. Introduction. A graph G consists of a set 7 of elements called vertices together with a set E of elements called edges, the two sets having no element in common. With each edge there are associated either one or two vertices called its ends. In this paper we consider only graphs in which each edge has two distinct ends. We call such a graph oriented if one end of each edge is distinguished a...
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An oriented graph is a directed graph which can be obtained from a simple undirected graph by orienting its edges. In this paper we show that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2 − o(1))n contains a packing of cyclic triangles covering all but at most 3 vertices. This almost answers a question of Cuckler and Yuster and is best possible, since for ...
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In this paper, we investigate the number of 1-factors of a generalized Petersen graph $P(N,k)$ and get a lower bound for the number of 1-factors of $P(N,k)$ as $k$ is odd, which shows that the number of 1-factors of $P(N,k)$ is exponential in this case and confirms a conjecture due to Lovász and Plummer (Ann. New York Acad. Sci. 576(2006), no. 1, 389-398).
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In this paper it is shown that if G is a connected graph of order 2n (n> 1) not containing a 1-factor, then for each k, Kk^n, there exists an induced, connected subgraph of order 2k which also fails to possess a 1-factor. Several other sufficient conditions for a graph to contain a 1-factor are presented. In particular, it is seen that the connected even order line graphs and total graphs alway...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1953
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1953-0063009-7