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...

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);...

the interval graphs, and the maximal outerplanar graphs. The split graphs are exactly the graphs that are chordal and have a chordal complement. The...

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...

graph is a forest. More advanced kinds of graphs are: Petersen graph and its generalizations; perfect graphs; cographs; chordal graphs; other graphs with...

graph; perfect graphs include many well-known graph classes including the bipartite graphs, chordal graphs, and comparability graphs. In his 1961 and...

unique smallest cubic graph of girth 8, it is a cage and a Moore graph. It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle...

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

which are also chordal. Just as chordal graphs are the intersection graphs of subtrees of trees, split graphs are the intersection graphs of distinct substars...

of the bipartition of a complete bipartite graph, every vertex on the other side is a median. Every chordal bipartite graph (a class of graphs that includes...

subgraphs of chordal graphs are not necessarily chordal, so being a chordal graph is not monotone. A graph property is minor-closed if every graph minor of...

added while preserving outerplanarity, are also chordal graphs and visibility graphs. Outerplanar graphs were first studied and named by Chartrand & Harary...

cluster graph is a graph whose connected components are cliques. A block graph is a graph whose biconnected components are cliques. A chordal graph is a...

particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as...

classes of graphs, such as forests, chordal graphs, cycles, wheels, and ladders, so these can be evaluated in polynomial time. If the graph is planar and...

of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology. Amalgamation Bipartite graph Complete bipartite graph Disperser...

bounded-degree planar graphs, split graphs, bipartite graphs and their complements, line graphs of bipartite graphs, unit disk graphs, interval graphs of diameter...

greater than three. A chordal graph, a special type of perfect graph, has no holes of any size greater than three. The girth of a graph is the length of its...

complete bipartite graph K3,3. For Kuratowski's theorem, the notion of containment is that of graph homeomorphism, in which a subdivision of one graph appears...

graph are transitive. Every bipartite graph is also a comparability graph. Orienting the edges of a bipartite graph from one side of the bipartition to...

complements of comparability graphs, and trapezoid graphs. The subclasses of the permutation graphs include the bipartite permutation graphs (characterized by Spinrad...

that out of all bipartite graphs, crown graphs require longest word-representants? Is the line graph of a non-word-representable graph always non-word-representable...

parity, and the line perfect graphs, a generalization of the bipartite graphs. Every parity graph is a Meyniel graph, a graph in which every odd cycle of...

associated bipartite graph by chain graphs (graphs with no induced 2K2). Using vertex splitting, the recognition problem for trapezoid graphs was shown...

for the whole graph. The complete bipartite graphs are the only connected graphs whose Grundy number is two. All other connected graphs contain either...

This conjecture is known to hold for chordal bipartite graphs, bipartite series–parallel graphs, and bipartite graphs of maximum degree three. The conjecture...

still unproven, weakens Tait's conjecture in a different way, to bipartite planar graphs. Tutte's original publication of the theorem in 1956 had a complicated...

The graph sandwich problem is NP-complete when Π is the property of being a chordal graph, comparability graph, permutation graph, chordal bipartite graph...

more general graph classes. Special types of cograph include complete graphs, complete bipartite graphs, cluster graphs, and threshold graphs. Cographs are...

Petersen graph is nonplanar. Any nonplanar graph has as minors either the complete graph K 5 {\displaystyle K_{5}} , or the complete bipartite graph K 3 ...