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The Turán graphs are the special case of complete multipartite graphs in which each two independent sets differ in size by at most one vertex. Complete k-partite graphs, complete multipartite graphs, and their complement graphs, the cluster graphs, are special cases of cographs, and can be recognized in polynomial time even when the partition ...
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The star graphs K 1,3, K 1,4, K 1,5, and K 1,6. A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars.
The complete bipartite graph <math>K_{2,1}</math>. Based on Image:Complete bipartite graph K3,3.svg by David Benbennick. {{PD-self}} Category:Graph theory: 15:01, 2 February 2007: 1,062 × 805 (605 bytes) Illes: The complete bipartite graph <math>K_{2,1}</math>. Based on Image:Complete bipartite graph K3,3.svg by David Benbennick. {{PD-self ...
In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw.
A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. Odd cycle transversal is an NP-complete algorithmic problem that asks, given a graph G = (V,E) and a number k, whether there exists a set of k vertices whose removal from G would cause the resulting graph to be bipartite. [31]
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A complete bipartite graph in which has vertices and has vertices is denoted ,. If G = ( U ∪ V , E ) {\displaystyle G=(U\cup V,E)} is a bipartite graph, and there exists a set of s {\displaystyle s} vertices of U {\displaystyle U} and t {\displaystyle t} vertices of V {\displaystyle V} that are all connected to each other, then these vertices ...