Last edited by nodata
04.06.2021 | History

5 edition of Clique perfect graphs. found in the catalog. # Clique perfect graphs.

## Indices [compiled by F. Wormald]

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Classifications The Physical Object Statement nodata Publishers nodata LC Classifications 1988 Pagination xvi, 86 p. : Number of Pages 52 ISBN 10 nodata 1 nodata 2 3

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Thus, the edge v,w and vertices v, w and j form a subgraph of the path described above. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color equals the maximum number of cliques of H with a common vertex, for every induced subgraph H of G.

### terminology

Cambridge University Press, Cambridge 2011 Affiliations• In any partition of V into cliques, since each vertex of an independent I set must end up in a clique that contains no other member of I, the total number of blocks of the partition must be at least the maximum size of any I.

A line graph is a graph whose edges can be covered by edge-disjoint cliques in such a way that each vertex belongs to exactly two of the cliques in the cover. This is only possible when there are no edges that go between the subgraphs, since otherwise these edges will be lost in the partitioning, not being in any of the subgraphs.

Received : 09 November 2015• For example, if the vertices of the Clique perfect graphs. are, in order around the cycle1, 23, …, then 1,4 and 2,5 are examples of chordal bridges which cannot both be drawn on the same side of the cycle without a crossing.

### Bounding Clique

: Critical and anticritical edges in perfect graphs. But now if we also select all edges that were incident on the selected set of vertices in the original graph, then we construct an induced subgraph. We can see that by considering the graph Q, on 6 vertices, that can be described as a 5-cycle with another edge linking the sixth vertex to one vertex of the cycle. : Finding odd cycle transversals.

• , which are graphs that can be ordered in such a way that a algorithm is optimal on every induced subgraph.

• To prove boundedness of clique-width for the first three cases we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs.

• Let's consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance.