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The largest maximal clique is a maximum clique, and, as chordal graphs are perfect, the size of this clique equals the chromatic number of the chordal graph. Chordal graphs are perfectly orderable: an optimal coloring may be obtained by applying a greedy coloring algorithm to the vertices in the reverse of a perfect elimination ordering. [7]
In graph theory, an interval graph is an undirected graph formed from a set of intervals on the real line, with a vertex for each interval and an edge between vertices whose intervals intersect. It is the intersection graph of the intervals. Interval graphs are chordal graphs and perfect graphs.
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.
A graph is strongly chordal if and only if each of its induced subgraphs is a dually chordal graph. [6] Strongly chordal graphs may also be characterized in terms of the number of complete subgraphs each edge participates in. [7] Yet another characterization is given in. [8]
An overview of the different components included in the field of chemical biology. Chemical biology is a scientific discipline between the fields of chemistry and biology.The discipline involves the application of chemical techniques, analysis, and often small molecules produced through synthetic chemistry, to the study and manipulation of biological systems. [1]
A chordal graph is a graph whose vertices can be ordered into a perfect elimination ordering, an ordering such that the neighbors of each vertex v that come later than v in the ordering form a clique. A cograph is a graph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single ...
The split graphs are exactly the graphs that are chordal and have a chordal complement. [38] The k-trees, central to the definition of treewidth, are chordal graphs formed by starting with a (k + 1)-vertex clique and repeatedly adding a vertex so that it and its neighbors form a clique of the same size. [35]
Every perfectly orderable graph is a perfect graph. [1] Chordal graphs are perfectly orderable; a perfect ordering of a chordal graph may be found by reversing a perfect elimination ordering for the graph. Thus, applying greedy coloring to a perfect ordering provides an efficient algorithm for optimally coloring chordal graphs.