共查询到20条相似文献,搜索用时 15 毫秒
1.
Jie MaXingxing Yu 《Journal of Combinatorial Theory, Series B》2012,102(1):212-232
Bollobás and Thomason conjectured that the vertices of any r-uniform hypergraph with m edges can be partitioned into r sets so that each set meets at least rm/(2r−1) edges. For r=3, Bollobás, Reed and Thomason proved the lower bound (1−1/e)m/3≈0.21m, which was improved to (5/9)m by Bollobás and Scott and to 0.6m by Haslegrave. In this paper, we show that any 3-uniform hypergraph with m edges can be partitioned into 3 sets, each of which meets at least 0.65m−o(m) edges. 相似文献
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A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use to denote the 3-uniform hypergraph whose vertex set can be partitioned into two vertex classes and of size and , respectively, and whose edge set consists of all the triples containing at least two vertices of . Let be a 3-uniform hypergraph of order with no isolated vertex and for any two adjacent vertices . In this paper, we show that contains a matching of size if and only if is not a subgraph of . This result improves our previous one in Zhang and Lu (2018). 相似文献
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A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. A -matching in a 3-uniform hypergraph is a matching of size . Let be a partition of vertices such that and . Denote by the 3-uniform hypergraph with vertex set consisting of all those edges which contain at least two vertices of . Let be a 3-uniform hypergraph of order such that for any two adjacent vertices . In this paper, we prove contains a -matching if and only if is not a subgraph of . 相似文献
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CHENHUAITANG MAKEJIE 《高校应用数学学报(英文版)》1998,13(2):165-170
The definition of the ascending suhgraph decomposition was given by Alavi. It has been conjectured that every graph of positive size has an ascending subgraph decomposition. In this paper it is proved that the regular graphs under some conditions do have an ascending subgraph decomposition. 相似文献
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A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals overlap and at least one of them is a probe. PIGs are a generalization of interval graphs introduced by Zhang for an application concerning the physical mapping of DNA in the human genome project. PIGs have been characterized in the cycle-free case by Sheng, and other miscellaneous results are given by McMorris, Wang, and Zhang. Johnson and Spinrad give a polynomial time recognition algorithm for when the partition of vertices into probes and nonprobes is given. The complexity for the general recognition problem is not known. Here, we restrict attention to the case where all intervals have the same length, that is, we study the unit probe interval graphs and characterize the cycle-free graphs that are unit probe interval graphs via a list of forbidden induced subgraphs. 相似文献
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Mock threshold graphs are a simple generalization of threshold graphs that, like threshold graphs, are perfect graphs. Our main theorem is a characterization of mock threshold graphs by forbidden induced subgraphs. Other theorems characterize mock threshold graphs that are claw-free and that are line graphs. We also discuss relations with chordality and well-quasi-ordering as well as algorithmic aspects. 相似文献
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《Discrete Mathematics》2022,345(12):113057
Let H be a fixed graph. In this paper we consider the problem of edge decomposition of a graph into subgraphs isomorphic to H or (a 2-edge matching). We give a partial classification of the problems of existence of such decomposition according to the computational complexity. More specifically, for some large class of graphs H we show that this problem is polynomial time solvable and for some other large class of graphs it is NP-complete. These results can be viewed as some edge decomposition analogs of a result by Loebl and Poljak who classified according to the computational complexity the problem of existence of a graph factor with components isomorphic to H or . In the proofs of our results we apply so-called rooted packings into graphs which are mutual generalizations of both edge decompositions and factors of graphs. 相似文献
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We answer some of the questions raised by Golumbic, Lipshteyn and Stern and obtain some other results about edge intersection graphs of paths on a grid (EPG graphs). We show that for any d≥4, in order to represent every n vertex graph with maximum degree d as an edge intersection graph of n paths on a grid, a grid of area Θ(n2) is needed. We also show several results related to the classes Bk-EPG, where Bk-EPG denotes the class of graphs that have an EPG representation such that each path has at most k bends. In particular, we prove: For a fixed k and a sufficiently large n, the complete bipartite graph Km,n does not belong to B2m−3-EPG (it is known that this graph belongs to B2m−2-EPG); for any odd integer k we have Bk-EPG Bk+1-EPG; there is no number k such that all graphs belong to Bk-EPG; only 2O(knlog(kn)) out of all the labeled graphs with n vertices are in Bk-EPG. 相似文献
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In this paper, we investigate a generalization of graph decomposition, called hypergraph decomposition. We show that a decomposition of a 3-uniform hypergraph K(3)v into a special kind of hypergraph K(3)4 - e exists if and only if v ≡ 0, 1, 2 (mod 9) and v ≥ 9. 相似文献
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We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most cn, where c≈1.6702. The best known lower bound for this number, due to Tomescu, is adn, where d=101/5≈1.5849 and a is a constant. 相似文献
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A graph is polar if the vertex set can be partitioned into A and B in such a way that the subgraph induced by A is a complete multipartite graph and the subgraph induced by B is a disjoint union of cliques. Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. However, recognizing polar graphs is an NP-complete problem in general. This led to the study of the polarity of special classes of graphs such as cographs and chordal graphs, cf. Ekim et al. (2008) [7] and [5]. In this paper, we study the polarity of line graphs and call a graph line-polar if its line graph is polar. We characterize line-polar bipartite graphs in terms of forbidden subgraphs. This answers a question raised in the fist reference mentioned above. Our characterization has already been used to develop a linear time algorithm for recognizing line-polar bipartite graphs, cf. Ekim (submitted for publication) [6]. 相似文献
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The well‐known Friendship Theorem states that if G is a graph in which every pair of vertices has exactly one common neighbor, then G has a single vertex joined to all others (a “universal friend”). V. Sós defined an analogous friendship property for 3‐uniform hypergraphs, and gave a construction satisfying the friendship property that has a universal friend. We present new 3‐uniform hypergraphs on 8, 16, and 32 vertices that satisfy the friendship property without containing a universal friend. We also prove that if n ≤ 10 and n ≠ 8, then there are no friendship hypergraphs on n vertices without a universal friend. These results were obtained by computer search using integer programming. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 253–261, 2008 相似文献
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A subset of vertices in a graph is called a dissociation set if it induces a subgraph with a vertex degree of at most 1. The maximum dissociation set problem, i.e., the problem of finding a dissociation set of maximum size in a given graph is known to be NP-hard for bipartite graphs. We show that the maximum dissociation set problem is NP-hard for planar line graphs of planar bipartite graphs. In addition, we describe several polynomially solvable cases for the problem under consideration. One of them deals with the subclass of the so-called chair-free graphs. Furthermore, the related problem of finding a maximal (by inclusion) dissociation set of minimum size in a given graph is studied, and NP-hardness results for this problem, namely for weakly chordal and bipartite graphs, are derived. Finally, we provide inapproximability results for the dissociation set problems mentioned above. 相似文献
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Selçuk Kayacan 《代数通讯》2017,45(6):2466-2477
The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper we classify all finite groups whose intersection graphs are K3,3-free. 相似文献
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Selçuk Kayacan 《代数通讯》2018,46(4):1492-1505
The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper, we classify finite solvable groups whose intersection graphs are not 2-connected and finite nilpotent groups whose intersection graphs are not 3-connected. Our methods are elementary. 相似文献
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Shuchao Li 《Discrete Mathematics》2009,309(14):4843-2218
By applying a discharging method, we give new lower bounds for the sizes of edge chromatic critical graphs for small maximum degrees. Furthermore, it is also proved that if G is a graph embeddable in a surface S with characteristic cS=−4 or −5 or −6, then G is class one if its maximum degree Δ≥10 or 11 or 12 respectively. 相似文献