Примеры использования Bipartite graph на Английском языке и их переводы на Русский язык
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Therefore, no directed bipartite graph can be aperiodic.
The algorithm is easier to describe if we formulate the problem using a bipartite graph.
Every bipartite graph is also a comparability graph. .
The incidence graph of a generalized digon is a complete bipartite graph Ks+1,t+1.
The complete bipartite graph Km, n has edge covering number maxm, n.
The smallest 1-crossing cubic graph is the complete bipartite graph K3,3, with 6 vertices.
Every bipartite graph is of class 1, and almost all random graphs are of class 1.
The Turán graph T(n, 2)is a complete bipartite graph and, when n is even, a Moore graph. .
In fact, any near polygon that has precisely two points per line must be a connected bipartite graph.
However, every bipartite graph occurs as an induced subgraph of some hypohamiltonian graph. .
Hall's marriage theorem can be used to show that a k-regular bipartite graph contains a perfect matching.
In any bipartite graph, the number of edges in a maximum matching equals the number of vertices in a minimum vertex cover.
For instance, unboundedly chromatic graphs must also contain every possible finite bipartite graph as a subgraph.
The figure shows the complete bipartite graph K4,4, with the colors indicating a partition of its edges into three forests.
Coleman& Moré(1984) showed that finding an optimal star coloring is NP-hard even when G is a bipartite graph.
Every complete bipartite graph of the form K2,n is 1-planar, as is every complete tripartite graph of the form K1,1,n.
The incidence graph of a generalized quadrangle is characterized by being a connected, bipartite graph with diameter four and girth eight.
In a bipartite graph, all nodes that are not in the minimum vertex cover can be included in maximum independent set; see Kőnig's theorem.
These two graphs provide counterexamples to the conjecture of W. T. Tutte that every cubic 3-connected bipartite graph is Hamiltonian.
In particular, the conjecture is true when G orH is a bipartite graph, since then its chromatic number is either 1 or 2.
Any connected bipartite graph is a near polygon and any near polygon with precisely two points per line is a connected bipartite graph.
If the complete graph Kn+ 1 has a perfect 1-factorization,then the complete bipartite graph Kn, n also has a perfect 1-factorization.
Kőnig's theorem states that, in any bipartite graph, the number of edges in a maximum matching is equal to the number of vertices in a minimum vertex cover.
Specifically, every graph satisfying the conditions of Ore's theorem is either a regular complete bipartite graph or is pancyclic Bondy 1971.
For instance a complete bipartite graph K1,n has the same line graph as the dipole graph and Shannon multigraph with the same number of edges.
In the example above, the four topmost vertices induce a claw(that is,a complete bipartite graph K1,3), shown on the top left of the illustration of forbidden subgraphs.
In a bipartite graph with no isolated vertices, the number of vertices in a maximum independent set equals the number of edges in a minimum edge covering; this is Kőnig's theorem.
However, graphs of clique-width k that have no complete bipartite graph Kt, t as a subgraph have treewidth at most 3k(t- 1)- 1.
In a nontrivial bipartite graph, the optimal number of colors is(by definition) two, and(since bipartite graphs are triangle-free) the maximum clique size is also two.
However, a combinatorial metric does exist in the corresponding incidence graph(Levi graph), namely the length of the shortest path between two vertices in this bipartite graph.