2 edition of **A characterization of clique graphs** found in the catalog.

A characterization of clique graphs

Fred S. Roberts

- 335 Want to read
- 37 Currently reading

Published
**1969**
by Rand Corp. in Santa Monica, Calif
.

Written in English

- Graph theory.

**Edition Notes**

Statement | [by] Fred S. Roberts and Joel H. Spencer. |

Series | Rand Corporation. Memorandum RM-5933-PR |

Contributions | Spencer, Joel H., joint author. |

Classifications | |
---|---|

LC Classifications | Q180.A1 R36 no. 5933 |

The Physical Object | |

Pagination | vii, 20 p. |

Number of Pages | 20 |

ID Numbers | |

Open Library | OL5751447M |

LC Control Number | 71009911 |

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Barnes & Noble’s online bookstore for books, NOOK ebooks & magazines. Shop music, movies, toys & games, too. Receive free shipping with your Barnes & Noble g: clique graphs. Cliques and Colorings. Given an undirected graph G = (V, E), a clique of the graph is a set of mutually adjacent vertices. A maximum clique is, naturally, a clique whose number of vertices is at least as large as that for any other clique in the graph.

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A graph-theoretic discussion following up a recent paper in which Hamelink obtains an interesting sufficient condition for a graph to be a clique graph. In the present study related conditions are given that are necessary as well as by: A characterization of edge-clique graphs of out-erplanar graphs is given; a complete description of edge-clique graphs of threshold graphs is presented and a linear time algorithm for l-coloring.

A PARTIAL CHARACTERIZATION OF CLIQUE GRAPHS 5. CONCLUSION The answer to the question of whether a particular graph H is a clique graph depends, apparently, on the clique graph of H and the clique parti- tion of V(H).

The clique partition may also be of use in other parts of graph by: G = G 1 + G 2, give a characterization for clique con vergence of the join of graphs and if G 1, G 2 are Clique-Helly graphs diﬀerent from K 1 and G = G 1 G 2, then K 2 (G) = G.

Clique graphs of chordal and path graphs are characterized. A special class of graphs named expanded trees is discussed. It consists of a subclass of disk-Helly graphs. It is shown that the clique graph of every chordal (hence path) graph is an expanded tree. In addition, every expanded tree is the clique graph of some path (hence chordal) by: Say that G is a clique graph if there exists a graph H such that G=K(H).

The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink inand a characterization was proposed by Roberts A characterization of clique graphs book Spencer in We prove that the clique graph recognition problem is by: Given a factor graph F, its completion F is obtained by adding one factor node for each clique in the.

24In usual graph theory, the word clique refers to graph (recall that a graph is deﬁned by a set of nodes and a set of edges which join node pairs), rather than to factor Size: 1MB. The interactive Character Scrapbook is a great way to engage students and help them form a deeper understanding of a book's characters.

It works with almost any fiction or nonfiction book, and can be used individually or as a whole g: clique graphs. Finding All Cliques of an Undirected Graph Seminar „Current Trends in IE“ WS 06/07 Michaela Regneri 1. Motivation •How to put as much left-over stuff as possible in a tasty •the nodes already defined as part of the clique (compsub) (initially empty)File Size: KB.

their characterization of clique graphs. Escalante [3], among other results, showed that the clique graph of a Helly graph is Helly, and every Helly graph is the clique graph of some Helly graph.

If n denotes a class of graphs, then let K(17) denote the set of cliques of. Characterization of weighted clique graphs. The characterization of clique graphs is as follows.

Theorem 4 Roberts and Spencer, A graph H is a clique graph if and only if there is a collection F of complete sets of H such that every edge of H is contained in some complete set of F, and F satisfies the Helly by: 2.

Characterization. A graph H is the clique graph K (G) of another graph if and only if there exists a collection C of cliques in H whose union covers all the edges of H, such that C forms a Helly family.

This means that, if S is a subset of C with the property that every two. A characterization of edge-clique graphs of out-erplanar graphs is given; a complete description of edge-clique graphs of threshold graphs is presented and a linear time algorithm for l-coloring the edge-clique graph of a threshold graph is provided.

A survey on the l-coloring problem, when restricted to edge-clique graphs, is reported. clique number within any constant factor is NP-hard (in fact, we can also show the NP-hardness of approximating the clique number within a factor 2loge n, where n is the number of vertices in the graph and e is an arbitrarily small positive constant).

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INTRODUCTION. We consider simple, finite, undirected graphs. Given a graph G = (V, E), a complete set of G is a subset of V inducing a complete subgraph. A clique is a maximal complete be a family of subsets of a set say that satisfies the Helly property when every subfamily consisting of pairwise intersecting subsets has a non-empty intersection.

In this work, we present a structural result on probe 2-clique graphs that leads to a polynomial-time recognition algorithm for this class, and a forbidden induced subgraph characterization of probe diamond-free graphs implying a forbidden induced subgraph characterization for probe block graphs.