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...
Convex hulls of polyominoes.
Convex independence and the structure of clone-free multipartite tournaments
We investigate the convex invariants associated with two-path convexity in clone-free multipartite tournaments. Specifically, we explore the relationship between the Helly number, Radon number and rank of such digraphs. The main result is a structural theorem that describes the arc relationships among certain vertices associated with vertices of a given convexly independent set. We use this to prove that the Helly number, Radon number, and rank coincide in any clone-free bipartite tournament. We...
Convex Polytopes Whose Projection Bodies and Difference Sets Are Polars.
Convex Representations of Maps on the Torus and Other Flat Surfaces.
Convex universal fixers
In [1] Burger and Mynhardt introduced the idea of universal fixers. Let G = (V, E) be a graph with n vertices and G’ a copy of G. For a bijective function π: V(G) → V(G’), define the prism πG of G as follows: V(πG) = V(G) ∪ V(G’) and , where . Let γ(G) be the domination number of G. If γ(πG) = γ(G) for any bijective function π, then G is called a universal fixer. In [9] it is conjectured that the only universal fixers are the edgeless graphs K̅ₙ. In this work we generalize the concept of universal...
Convex-ear decompositions and the flag -vector.
Convolutions related to q-deformed commutativity
Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution of measures...
Cooperative guards in art galleries [Book]
Cooperative guards in art galleries with one hole.
Coordinatization of parallel systems. II.
Cordial deficiency.
Cores and shells of graphs
The -core of a graph , , is the maximal induced subgraph such that , if it exists. For , the -shell of a graph is the subgraph of induced by the edges contained in the -core and not contained in the -core. The core number of a vertex is the largest value for such that , and the maximum core number of a graph, , is the maximum of the core numbers of the vertices of . A graph is -monocore if . This paper discusses some basic results on the structure of -cores and -shells....
Correction de mon article ’Sur le nombre des -cycles dans un tournoi’
Correction: “The smallest graph whose group is cyclic”
Correction to "Partial Spreads in Finite Projective Spaces and Partial Designs".
Correction to "The bias of three pseudo-random shuffles", Volume 22, 2/3 (1981), p. 268-292.
Correction to the paper "A note on inequivalent Hadamard matrices".
Correction to the paper: Packing of 180 equal circles on a sphere. Elemente der Mathematik. Vol. 38, 1983, 119-122.