Uniquely restricted matchings in subcubic graphs without short cycles
نویسندگان
چکیده
منابع مشابه
Uniquely Restricted Matchings in Interval Graphs
A matching M in a graph G is said to be uniquely restricted if there is no other matching in G that matches the same set of vertices as M . We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted matching in an interval graph, thereby answering a question of Golumbic et al. (“Uniquely restricted matchings”, M. C. Golumbic, T. Hirst and M. Lewenstein, Algorit...
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A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on c...
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A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. This notion was defined by Golumbic, Hirst, and Lewenstein and studied in a number of articles. Our contribution is twofold. We provide approximation algorithms for computing a uniquely restricted matching of maximum size in some bipartite graphs. In particular, we achieve a ratio of 9/5 f...
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For a directed graph G without loops or parallel edges, let β(G) denote the size of the smallest feedback arc set, i.e., the smallest subset X ⊂ E(G) such that G \X has no directed cycles. Let γ(G) be the number of unordered pairs of vertices of G which are not adjacent. We prove that every directed graph whose shortest directed cycle has length at least r ≥ 4 satisfies β(G) ≤ cγ(G)/r, where c ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2020
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22632