Constructive lower bounds on classical multicolor Ramsey numbers.
Constructive upper bounds for cycle-saturated graphs of minimum size.
Containers and wide diameters of
The intersection graph of a graph has for vertices all the induced paths of order 3 in . Two vertices in are adjacent if the corresponding paths in are not disjoint. A -container between two different vertices and in a graph is a set of internally vertex disjoint paths between and . The length of a container is the length of the longest path in it. The -wide diameter of is the minimum number such that there is a -container of length at most between any pair of different...
Continuation of a 3-coloring from a 7-face onto a plane graph without .
Continued fractions and Catalan problems.
Continuity of the percolation threshold in randomly grown graphs.
Continuous homomorphisms on and Ramsey theory.
Continuous monoids and yields of infinite trees
Contractible edges in some -connected graphs
An edge of a -connected graph is said to be -contractible (or simply contractible) if the graph obtained from by contracting (i.e., deleting and identifying its ends, finally, replacing each of the resulting pairs of double edges by a single edge) is still -connected. In 2002, Kawarabayashi proved that for any odd integer , if is a -connected graph and contains no subgraph , then has a -contractible edge. In this paper, by generalizing this result, we prove that for any integer...
Contraction distance between isomorphism classes of graphs
Contravariant functors on finite sets and Stirling numbers.
Contribution of František Matúš to the research on conditional independence
An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract...
Contribution to the problem of the spectra of compound graphs.
Control flow graphs and code coverage
The control flow of programs can be represented by directed graphs. In this paper we provide a uniform and detailed formal basis for control flow graphs combining known definitions and results with new aspects. Two graph reductions are defined using only syntactical information about the graphs, but no semantical information about the represented programs. We prove some properties of reduced graphs and also about the paths in reduced graphs. Based on graphs, we define statement coverage and branch...
Control treatments in designs with split units generated by Latin squares
This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments...
Controllable graphs
Converse mean value theorems on trees and symmetric spaces.
Converting between generalized Bell, Lah, Stirling, and Tanh numbers.
Convex 4-valent polytopes with prescribed types of faces
Convex domination in the composition and Cartesian product of graphs
In this paper we characterize the convex dominating sets in the composition and Cartesian product of two connected graphs. The concepts of clique dominating set and clique domination number of a graph are defined. It is shown that the convex domination number of a composition of two non-complete connected graphs and is equal to the clique domination number of . The convex domination number of the Cartesian product of two connected graphs is related to the convex domination numbers of the...