Graph theory claw

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August undefined, 2024

WebMar 24, 2024 · A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and … WebA line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a simple …

Claw Graph -- from Wolfram MathWorld

WebA graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way. WebA suucient condition for hamiltonicity in claw-free graphs, the equivalence of some conjectures on ham Miltonicity in 2-tough graphs and the Hamiltonicity of 7-connected … slow flute solos

Line graph - Wikipedia

WebOct 12, 2024 · Since \(\Gamma (G) \ge \alpha (G)\) for all graphs G, the following lower bound on the upper domination number of a claw-free cubic graph follows from Observation 1.. Observation 2. If \(G \ne K_4\) is a connected claw-free graph of order n, then \(\Gamma (G) \ge \frac{1}{3}n\).. As a consequence of the characterizations given in [], we can … WebAug 28, 2008 · A set S of vertices in a graph G is a total dominating set, denoted by TDS, of G if every vertex of G is adjacent to some vertex in S (other than itself). The minimum cardinality of a TDS of G is the total domination number of G, denoted by γ t (G).If G does not contain K 1, 3 as an induced subgraph, then G is said to be claw-free. It is shown in … WebDec 1, 2024 · , The strong perfect graph conjecture is true for K 1 , 3-free graphs, J. Comb. Theory Ser. B 21 (1976) 212 – 223. Google Scholar [25] Rao M., MSOL partitioning problems on graphs of bounded treewidth and clique-width, Theoret. Comput. Sci. 377 (2007) 260 – 267. Google Scholar software for printing industry

The structure of claw-free perfect graphs — Princeton …

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WebNov 1, 1991 · A graph is claw-free if it contains no induced subgraph isomorphic to a K 1,3.This paper studies hamiltonicity in two subclasses of claw-free graphs. A claw-free graph is CN-free (claw-free, net-free) if it does not contain an induced subgraph isomorphic to a net (a triangle with a pendant leaf dangling from each vertex). We give a structural … WebIn graph theory, a -bounded family of graphs is one for which there is some function such that, for every integer the graphs in with = (clique number) can be colored with at most () colors. This concept and its notation were formulated by András Gyárfás. The use of the Greek letter chi in the term -bounded is based on the fact that the chromatic number of a … software for printing stylish envelopesWebIn 1999, Maffray and Reed (J Combin Theory Ser B 75 (1) (1999), 134-156) successfully described how elementary graphs can be built using line-graphs of bipartite graphs using … software for printrbot simple metal 14.07l

"A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph. See more In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the complete bipartite graph K1,3 (that is, a star graph comprising three … See more Because claw-free graphs include complements of triangle-free graphs, the number of claw-free graphs on n vertices grows at least as quickly as the number of triangle-free … See more An independent set in a line graph corresponds to a matching in its underlying graph, a set of edges no two of which share an endpoint. The blossom algorithm of Edmonds (1965) finds a maximum matching in any graph in polynomial time, … See more • The line graph L(G) of any graph G is claw-free; L(G) has a vertex for every edge of G, and vertices are adjacent in L(G) whenever the … See more It is straightforward to verify that a given graph with n vertices and m edges is claw-free in time O(n ), by testing each 4-tuple of vertices to determine whether they induce a claw. With … See more Sumner (1974) and, independently, Las Vergnas (1975) proved that every claw-free connected graph with an even number of vertices has a perfect matching. That is, there exists a set of edges in the graph such that each vertex is an endpoint of exactly one of the … See more A perfect graph is a graph in which the chromatic number and the size of the maximum clique are equal, and in which this equality … See more " - Graph theory claw

Claw Graph -- from Wolfram MathWorld

Line graph - Wikipedia

Graph theory claw

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