Matchings in 1?planar graphs with large minimum degree
نویسندگان
چکیده
In 1979, Nishizeki and Baybars showed that every planar graph with minimum degree 3 has a matching of size n + c (where the constant depends on connectivity), even better bounds hold for graphs 4 5. this paper, we investigate similar matching-bounds 1-planar graphs, is, can be drawn such edge at most one crossing. We show least 1 7 12 , is tight some graphs. provide 5, while case 6 remains open.
منابع مشابه
Computing Large Matchings in Planar Graphs with Fixed Minimum Degree
In this paper we present algorithms that compute large matchings in planar graphs with fixed minimum degree. The algorithms give a guarantee on the size of the computed matching and run in linear time. Thus they are faster than the best known algorithm for computing maximum matchings in general graphs and in planar graphs, which run in O( √ nm) and O(n) time, respectively. For the class of plan...
متن کاملMatchings in hypergraphs of large minimum degree
It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for hypergraphs. We also prove several related results which guarantee the existence of almost perfect matchings in r-uniform hypergraphs of large minimum degree. Our bounds on the minimum degree are essentially best poss...
متن کاملPerfect matchings in uniform hypergraphs with large minimum degree
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a perfect matching in terms of a variant of the minimum degree. We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k − 1 vertices ...
متن کاملDiameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
متن کاملConnectivity keeping edges in graphs with large minimum degree
The old well-known result of Chartrand, Kaugars and Lick [1] says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G− v is still k-connected. In this paper, we consider a generalization of the above result. We prove the following result: Suppose G is a k-connected graph with minimum degree at least 3k/2 + 2. Then G has an edge e such that G− V (e) is sti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2021
ISSN: ['0364-9024', '1097-0118']
DOI: https://doi.org/10.1002/jgt.22736