Results 21 to 30 of about 92,446 (202)
Non-Bipartite K-Common Graphs [PDF]
Combinatorica, 2022 A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for
Králʼ, Daniel +4 more
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Rainbow perfect matchings in r-partite graph structures [PDF]
, 2016 A matching M in an edge–colored (hyper)graph is rainbow if each pair of edges in M have distinct colors. We extend the result of Erdos and Spencer on the existence of rainbow perfect matchings in the complete bipartite graph Kn,n to complete bipartite ...
Cano Vila, María del Pilar +2 more
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IEEE Access, 2019 Community detection has become a hot topic in complex networks. It plays an important role in information recommendation and public opinion control. Bipartite network, as a special complex network, reflects the characteristics of a kind of network in our
Furong Chang +4 more
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Journal of Function Spaces, 2022 Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences.
A. El-Mesady +2 more
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Inverses of Bipartite Graphs [PDF]
Combinatorica, 2017 Let $G$ be a bipartite graph and its adjacency matrix $\mathbb A$. If $G$ has a unique perfect matching, then $\mathbb A$ has an inverse $\mathbb A^{-1}$ which is a symmetric integral matrix, and hence the adjacency matrix of a multigraph. The inverses of bipartite graphs with unique perfect matchings have a strong connection to M bius functions of ...
Yang, Yujun, Ye, Dong
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Role coloring bipartite graphs
Discrete Applied Mathematics, 2022 A k-role coloring of a graph G is an assignment of k colors to the vertices of G such that if any two vertices are assigned the same color, then their neighborhood are assigned the same set of colors. By definition, every graph on n vertices admits an n-role coloring.
Sukanya Pandey, Vibha Sahlot
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Bounds for the Kirchhoff Index of Bipartite Graphs
Journal of Applied Mathematics, 2012 A -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent ...
Yujun Yang
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Orthogonal double cover of Complete Bipartite Graph by disjoint union of complete bipartite graphs
Ain Shams Engineering Journal, 2015 Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex, G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members share an edge whenever the corresponding ...
S. El-Serafi +2 more
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Bipartite powers of k-chordal graphs [PDF]
, 2012 Let k be an integer and k \geq 3. A graph G is k-chordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3-chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive
Chandran, L. Sunil, Mathew, Rogers
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A Note on a Binary Relation Corresponding to a Bipartite Graph
ITM Web of Conferences, 2018 In this paper, we firstly define a binary relation corresponding to the bipartite graph and study its properties. We also establish a relationship between the independent sets of the bipartite graph and the definable sets of binary relations ...
Sarı Hatice Kübra, Kopuzlu Abdullah
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