Generalized covering designs and clique coverings
نویسندگان
چکیده
Inspired by the “generalized t-designs” defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructing them, which in some cases we prove are optimal. Many of our results are obtained from an interpretation of these designs in terms of clique coverings of graphs.
منابع مشابه
On subgroups of topologized fundamental groups and generalized coverings
In this paper, we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology. Moreover, we present some conditions unde...
متن کاملClique Coverings of Glued Graphs at Complete Clones
A clique covering of a graph G is a set of cliques of G in which each edge of G is contained in at least one clique. The smallest cardinality of clique coverings of G is called the clique covering number of G. A glued graph results from combining two nontrivial vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the c...
متن کاملGeneralized clique coverings of chordal graphs
Two main types 1)£ clique coveri cd phs ha'J(? d j,scussed. One is ali que c C) v p r i r, 9 Cl f \! l-''', ice S , a set ,-, f clIques which between them contain eve! 'JI? te:,c at once. The other, a clique c:-overing of edgEs, is a set f cliques which between them contain eVPIY e0ge. CllVering of edges may be deflned as a lique covering of vertices with the added rest iction hat tho=> I:'"nds...
متن کاملInvited Talks
In 2009, Peter Cameron introduced a common generalization of various classes of combinatorial designs such as balanced incomplete block designs, resolvable designs and orthogonal arrays. Generalized covering and packing designs can be defined in analogous way. These objects bring into this framework further classes of designs, including covering and packing arrays, Howell designs, monogamous cy...
متن کاملClique coverings and partitions of line graphs
A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C. The clique covering (partition) number cc(G) (cp(G)) of G is the minimum size of a clique covering (partition) of G. This paper gives alternative proofs, using a unified approach, for the results on the clique c...
متن کامل