In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances...

disjoint union of graphs. The graphs that are both chordal and distance-hereditary are called Ptolemaic graphs, because their distances obey Ptolemy's inequality...

circle graphs as a special case. Every distance-hereditary graph is a circle graph, as is every permutation graph and every indifference graph. Every...

graphs are exactly the graphs that are both chordal and distance-hereditary; they include the block graphs and are a subclass of the perfect graphs....

graphs. They are also the Ptolemaic graphs (chordal distance-hereditary graphs) in which every two nodes at distance two from each other are connected by...

in turn, special cases of the distance-hereditary graphs, permutation graphs, comparability graphs, and perfect graphs. Any cograph may be constructed...

Meyniel graphs contain the chordal graphs, the parity graphs, and their subclasses the interval graphs, distance-hereditary graphs, bipartite graphs, and...

to be at distance one, they may also be called strict unit distance graphs or faithful unit distance graphs. As a hereditary family of graphs, they can...

i to label j (denoted by ρ(i,j)) Graphs of bounded clique-width include the cographs and distance-hereditary graphs. Although it is NP-hard to compute...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

graphs nor distance hereditary graphs satisfy any of these properties, even weaker versions. For (D ′ {\textstyle '} T) counterexample see the graph on...

used for fast recognition of circle graphs and distance-hereditary graphs, as well as for other problems in graph algorithms. Splits and split decompositions...

related graph removal lemmas is elaborated on below. For a graph G with n vertices, the notion of distance we will use is the edit distance. That is...

unweighted interval graph can be constructed in linear time. A polynomial time algorithm is also known for distance-hereditary graphs, weighted so that...

subroutine in other graph algorithms including the recognition of chordal graphs, and optimal coloring of distance-hereditary graphs. The breadth-first...

graph. Perfectly orderable graphs form a special case of the perfect graphs, and they include the chordal graphs, comparability graphs, and distance-hereditary...

in distance-hereditary graphs, every induced path is a shortest path. Induced cycles are induced subgraphs that are cycles. The girth of a graph is defined...

bipartite distance-hereditary graphs. Thus, half-graphs are distance-hereditary. That is, in every connected induced subgraph of a half-graph, the distances are...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

bipartite graphs and the bipartite distance-hereditary graphs) is modular. Modular graphs, Information System on Graph Classes and their Inclusions, retrieved...

perfect graph theorem, the perfect graphs are the graphs with no odd hole and no odd antihole. The distance-hereditary graphs are the graphs in which...

polynomial time for graphs of bounded clique-width. These include, among other graphs, the cographs and distance-hereditary graphs, which are also classes...

chordal graphs that are split approaches one. Ptolemaic graphs are graphs that are both chordal and distance hereditary. Quasi-threshold graphs are a subclass...

treewidth or bounded clique-width, such as the distance-hereditary graphs. Finally, it is clearly NP-hard on all graph classes on which the Hamiltonian path problem...

celebrated proof of the perfect graph theorem (Golumbic, 1980). For recognizing distance-hereditary graphs and circle graphs, a further generalization of...

length. This class of graphs was named and first studied by Burlet & Uhry (1984). Parity graphs include the distance-hereditary graphs, in which every two...

graph families that contain the bipartite distance-hereditary graphs, including the bipartite graphs, chordal bipartite graphs, distance-hereditary graphs...

In graph theory, a cop-win graph is an undirected graph on which the pursuer (cop) can always win a pursuit–evasion game against a robber, with the players...

bipartite graph is a modular graph. The chordal bipartite graphs include the complete bipartite graphs and the bipartite distance-hereditary graphs. Golumbic...

rank-width. These graphs include, for instance, the distance-hereditary graphs, the k-leaf powers for bounded values of k, and the graphs of bounded treewidth...