theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition (without...
4 KB (493 words) - 20:25, 28 July 2024
the complement of the Petersen graph, which can also be formed as the bipartite half of the 20-vertex Desargues graph. There are several different ways of...
10 KB (1,203 words) - 11:19, 3 August 2024
combinatorially as the "half-squares of planar bipartite graphs". That is, let G = (U,V,E) be a planar bipartite graph, with bipartition (U,V). The square of...
7 KB (778 words) - 06:49, 2 June 2023
mathematics, a half graph is a special type of bipartite graph. These graphs are called the half graphs because they have approximately half of the edges...
9 KB (1,203 words) - 02:38, 29 July 2024
In graph theory, the bipartite double cover of an undirected graph G is a bipartite, covering graph of G, with twice as many vertices as G. It can be constructed...
11 KB (1,435 words) - 22:51, 15 July 2023
whose Foster census of cubic symmetric graphs included this graph. The bipartite half of the Foster graph is a distance-regular graph and a locally linear...
5 KB (530 words) - 06:49, 27 February 2024
Maximum cut (redirect from Bipartite subgraph)
complementary subset is as large as possible. Equivalently, one wants a bipartite subgraph of the graph with as many edges as possible. There is a more...
22 KB (2,802 words) - 11:37, 12 August 2024
The bipartite realization problem is a classical decision problem in graph theory, a branch of combinatorics. Given two finite sequences ( a 1 , … , a...
5 KB (611 words) - 16:24, 14 August 2024
Cubic function (redirect from Bipartite Cubic)
to its inflection point; that is, it is invariant under a rotation of a half turn around this point. Up to an affine transformation, there are only three...
12 KB (1,746 words) - 17:03, 28 August 2024
theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is half-transitive...
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of bipartite graphs are perfect. Examples include the rook's graphs, the line graphs of complete bipartite graphs. Every line graph of a bipartite graph...
59 KB (7,042 words) - 19:21, 6 May 2024
Kőnig's theorem (graph theory) (category Bipartite graphs)
the maximum matching problem and the minimum vertex cover problem in bipartite graphs. It was discovered independently, also in 1931, by Jenő Egerváry...
24 KB (3,433 words) - 00:05, 30 April 2024
5-dimensional uniform 5-polytope, the 5-demicube. Because it is the bipartite half of a distance-regular graph, the halved cube graph is itself distance-regular...
8 KB (740 words) - 16:29, 19 September 2022
together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions...
6 KB (755 words) - 16:48, 9 April 2024
square root of G2. The half-square of a bipartite graph is the subgraph of its square induced by one side of the bipartition. 2. A squaregraph is a...
107 KB (15,784 words) - 17:42, 20 August 2024
a bipartite graph is perfect (see Kőnig's theorem), but need not be bipartite as the example of the claw graph shows. The line graphs of bipartite graphs...
43 KB (5,299 words) - 10:28, 5 July 2024
Graphon (section Complete bipartite graphon)
sequence ( H n ) {\displaystyle (H_{n})} of half-graphs, defined by taking H n {\displaystyle H_{n}} to be the bipartite graph on 2 n {\displaystyle 2n} vertices...
33 KB (5,459 words) - 18:45, 26 April 2024
815 = 5 × 163, number of graphs with 8 vertices and a distinguished bipartite block 816 = 24 × 3 × 17, tetrahedral number, Padovan number, Zuckerman...
22 KB (3,851 words) - 10:39, 19 August 2024
a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices representing the...
25 KB (2,748 words) - 05:23, 28 April 2024
two vertices, one on each side of the bipartition, such that each of these two vertices belongs to at most half of the graph's maximal independent sets...
16 KB (2,317 words) - 15:35, 16 July 2024
example is a special case of the following general theorem:: 274 G is a bipartite graph if-and-only-if MP(G) = FMP(G) if-and-only-if all corners of FMP(G)...
11 KB (1,552 words) - 21:50, 26 June 2024
half of the vertices. This definition includes the rooted products of a graph G and a one-edge graph. It also includes, for instance, the bipartite well-covered...
28 KB (3,372 words) - 07:42, 18 July 2024
exempt w/o = Walkover r = Retired d = Defaulted SR = Special ranking BPC = Bipartite Invitation "Wheelchair Tennis - Men's Singles Schedule". Tokyo 2020 Paralympics...
23 KB (208 words) - 23:45, 10 February 2024
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the...
14 KB (1,617 words) - 07:10, 6 December 2023
coloring algorithm will use three colors for the whole graph. The complete bipartite graphs are the only connected graphs whose Grundy number is two. All other...
12 KB (1,355 words) - 07:49, 16 July 2024
most 3. For bipartite graphs, the equivalence between vertex cover and maximum matching described by Kőnig's theorem allows the bipartite vertex cover...
22 KB (2,554 words) - 12:16, 12 August 2024
prematurely ended after it was revealed that he needed surgery to repair a bipartite patella. He finished the season batting .286/.343/.505 with 18 home runs...
186 KB (17,025 words) - 17:33, 30 August 2024
Rainbow matching (section In complete bipartite graphs)
connection to transversals of Latin squares. Denote by Kn,n the complete bipartite graph on n + n vertices. Every proper n-edge coloring of Kn,n corresponds...
21 KB (2,561 words) - 06:53, 22 July 2024
these graphs are bipartite and have Hamiltonian paths, their maximum independent sets have a number of vertices that is equal to half of the number of...
15 KB (1,727 words) - 18:10, 23 August 2024
graphs with an even number of vertices 2n, are the evenly split complete bipartite graphs Kn,n and the crown graphs on 2n vertices. Many other symmetric...
11 KB (1,158 words) - 12:55, 15 May 2023