Graph theory claw
WebIn the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the … 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
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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 … WebIn graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.. A …
WebOct 5, 2006 · In this thesis, we work on generalizations of hamiltonian graph theory, and focus on the following topics: hamiltonian, pancyclicity, chorded pancyclic in the claw-free graphs, k-fan-connected graphs. WebGiven a graph G, a Hamilton cycle of G is a cycle which visits all vertices of G. We will say that G is Hamiltonian if it contains a Hamilton cycle. Determining the Hamiltonicity of a graph is a classically difficult problem in graph theory. An old result due to Ore [33] states that every graph with n vertices and more than n−1 2 + 1 edges is ...
WebMar 24, 2024 · In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle … WebApr 15, 1998 · Theorem 2(ii) implies a result due to Oberly and Sumner [4], who proved that a connected claw-free graph on n>~3 vertices is hamiltonian if every vertex has a …
WebMay 1, 2007 · The independence polynomial of a graph G is the polynomial ∑ A x A , summed over all independent subsets A ⊆ V (G).We prove that if G is clawfree, then all the roots of its independence polynomial are real. This extends a theorem of Heilmann and Lieb [O.J. Heilmann, E.H. Lieb, Theory of monomer–dimer systems, Comm. Math. Phys. 25 …
WebAlgebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants . chip carving letteringWebJournal of Graph Theory. Volume 12, Issue 2 p. 209-216. Article. Hamilton cycles in claw-free graphs. Cun-Quan ... we are going to prove that, if G is a k-connected claw-free (K 1,3-free) graph of order n such that for any (k + 1)-independent set /, then G contains a Hamilton cycle. The theorem in this paper implies Bondy's conjecture in the ... grant high school softball fieldWebWe introduce a closure concept that turns a claw-free graph into the line graph of a multigraph while preserving its (non-)Hamilton-connectedness. As an application, we show that every 7-connected claw-free graph is Hamilton-connected, and we show that ... chip carving oakWebNov 1, 2012 · In 1988, Chvátal and Sbihi (J Combin Theory Ser B 44(2) (1988), 154–176) proved a decomposition theorem for claw-free perfect graphs. ... A graph is claw-free if no vertex has three pairwise ... grant high school yearbookWebThis treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. ... discussing set graphs and set-theoretic representations of claw-free graphs; investigates when ... grant high school track and fieldWebA 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 … chip carving oval plateWebWe show that, in a claw-free graph, Hamilton-connectedness is preserved under the operation of local completion performed at a vertex with 2-connected neighborhood. This result proves a conjecture ... grant high school reunion