Sphericity, cubicity, and edge clique covers of graphs
نویسندگان
چکیده
منابع مشابه
Sphericity, cubicity, and edge clique covers of graphs
The sphericity sph(G) of a graph G is the minimum dimension d for which G is the intersection graph of a family of congruent spheres in Rd . The edge clique cover number (G) is the minimum cardinality of a set of cliques (complete subgraphs) that covers all edges of G. We prove that if G has at least one edge, then sph(G) (G). Our upper bound remains valid for intersection graphs defined by bal...
متن کاملRegular clique covers of graphs
A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect in exactly p vertices. A graph G is said to have a p-regular k-clique cover if there is a p-regular family H of k-cliques of G such that each edge of G belongs to a clique in H. Such a p-regular kclique cover is separable if the complete subgraphs of order p that arise as intersections of pairs o...
متن کاملEdge clique graphs and some classes of chordal graphs
The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. We describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlike-threshold, split and threshold graphs. In particular, a known necessary condition for a graph to be an edge c...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2006
ISSN: 0166-218X
DOI: 10.1016/j.dam.2006.01.004