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Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph , a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced cycles.
In graph theory, a branch of mathematics, a chordal completion of a given undirected graph G is a chordal graph, on the same vertex set, that has G as a subgraph. A minimal chordal completion is a chordal completion such that any graph formed by removing an edge would no longer be a chordal completion.
In the mathematical area of graph theory, an undirected graph G is strongly chordal if it is a chordal graph and every cycle of even length (≥ 6) in G has an odd chord, i.e., an edge that connects two vertices that are an odd distance (>1) apart from each other in the cycle.
Dirac's theorem on chordal graphs, the characterization of chordal graphs as graphs in which all minimal separators are cliques; Dirac's theorem on cycles in k-connected graphs, the result that for every set of k vertices in a k-vertex-connected graph there exists a cycle that passes through all the vertices in the set
Actually, leaf powers form a proper subclass of strongly chordal graphs; a graph is a leaf power if and only if it is a fixed tolerance NeST graph [3] and such graphs are a proper subclass of strongly chordal graphs. [4] In Brandstädt et al. (2010) it is shown that interval graphs and the larger class of rooted directed path graphs are leaf ...
In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has a chord, i.e., an edge that connects two vertices that are a distance > 1 apart from each other in the cycle.
Treewidth may be formally defined in several equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal completion of the graph, in terms of the maximum order of a haven describing a strategy for a pursuit–evasion game on the graph, or in terms ...
3. A strongly chordal graph is a chordal graph in which every cycle of length six or more has an odd chord. 4. A chordal bipartite graph is not chordal (unless it is a forest); it is a bipartite graph in which every cycle of six or more vertices has a chord, so the only induced cycles are 4-cycles. 5.