Classification of six-point metrics.
Classification of tensor products of symmetric graphs
In the category of symmetric graphs there are exactly five closed tensor products. If we omit the requirement of units, we obtain twelve more.
Classification of the Steiner quadruple systems of cardinality 32
Classifying descents according to equivalence .
Classifying trees with edge-deleted central appendage number 2
The eccentricity of a vertex of a connected graph is the distance from to a vertex farthest from in . The center of is the subgraph of induced by the vertices having minimum eccentricity. For a vertex in a 2-edge-connected graph , the edge-deleted eccentricity of is defined to be the maximum eccentricity of in over all edges of . The edge-deleted center of is the subgraph induced by those vertices of having minimum edge-deleted eccentricity. The edge-deleted central...
Class-uniformly resolvable group divisible structures. I: Resolvable group divisible designs.
Class-uniformly resolvable group divisible structures. II: Frames.
Climbing elements in finite Coxeter groups.
Clique graph representations of ptolemaic graphs
A graph is ptolemaic if and only if it is both chordal and distance-hereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). The second intersection graph representation can also be generated from the clique graph, as a very special...
Clique irreducibility of some iterative classes of graphs
In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph,...
Clique packings and clique partitions of graphs without odd chordless cycles
In this paper we consider partitions (resp. packings) of graphs without odd chordless cycles into cliques of order at least 2. We give a structure theorem, min-max results and characterization theorems for this kind of partitions and packings.
Clique partitioning of interval graphs with submodular costs on the cliques
Given a graph G = (V,E) and a “cost function” (provided by an oracle), the problem [PCliqW] consists in finding a partition into cliques of V(G) of minimum cost. Here, the cost of a partition is the sum of the costs of the cliques in the partition. We provide a polynomial time dynamic program for the case where G is an interval graph and f belongs to a subclass of submodular set functions, which we call “value-polymatroidal”. This provides a common solution for various generalizations of the...
Clique parts independent of remainders
Clique-connecting forest and stable set polytopes
Let G = (V,E) be a simple undirected graph. A forest F ⊆ E of G is said to be clique-connecting if each tree of F spans a clique of G. This paper adresses the clique-connecting forest polytope. First we give a formulation and a polynomial time separation algorithm. Then we show that the nontrivial nondegenerate facets of the stable set polytope are facets of the clique-connecting polytope. Finally we introduce a family of rank inequalities which are facets, and which generalize the clique inequalities. ...
Cliques and Claws in Edge-transitive Strongly Regular Graphs.
Clique-width and the speed of hereditary properties.
Clopen graphs
A graph G on a topological space X as its set of vertices is clopen if the edge relation of G is a clopen subset of X² without the diagonal. We study clopen graphs on Polish spaces in terms of their finite induced subgraphs and obtain information about their cochromatic numbers. In this context we investigate modular profinite graphs, a class of graphs obtained from finite graphs by taking inverse limits. This continues the investigation of continuous colorings on Polish spaces and their homogeneity...
Closed Formulae for the Strong Metric Dimension of Lexicographi
Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension...
Closed k-stop distance in graphs
The Traveling Salesman Problem (TSP) is still one of the most researched topics in computational mathematics, and we introduce a variant of it, namely the study of the closed k-walks in graphs. We search for a shortest closed route visiting k cities in a non complete graph without weights. This motivates the following definition. Given a set of k distinct vertices = x₁, x₂, ...,xₖ in a simple graph G, the closed k-stop-distance of set is defined to be , where () is the set of all permutations from...
Closed walks in coset graphs and vertex-transitive non-Cayley graphs.