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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 complete bipartite graph K m,n has a maximum matching of size min{m,n}. A complete bipartite graph K n,n has a proper n-edge-coloring corresponding to a Latin square. [14] Every complete bipartite graph is a modular graph: every triple of vertices has a median that belongs to shortest paths between each pair of vertices. [15]
Douglas Brent West is a professor of graph theory at University of Illinois at Urbana-Champaign. He received his Ph.D. from Massachusetts Institute of Technology in 1978; his advisor was Daniel Kleitman. [1] He is the "W" in G. W. Peck, a pseudonym for a group of six mathematicians that includes West. [2]
A complete bipartite graph with m = 5 and n = 3 The Heawood graph is bipartite.. In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in .
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph.A graph is prime if it has no splits. The splits of a graph can be collected into a tree-like structure called the split decomposition or join decomposition, which can be constructed in linear time.
Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian-British mathematician who mainly worked in graph theory. [1] He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin from 1964 to 1966. [2] In 1952, he gave a sufficient condition for a graph to contain a Hamiltonian circuit.
In the mathematical field of graph theory, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least three distinct colors. Equivalently, in a star coloring, the induced subgraphs formed by the vertices of any two colors has connected components that are star graphs .