The component distribution of saturated subgraphs of families of trees. (Die Komponentenverteilung von gesättigten Teilgraphen in Baumfamilien.)
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].
The compositional construction of Markov processes II
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters, arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
The compositions of differential operations and the Gâteaux directional derivative.
The concept of Bailey chains.
The concept of cutting vectors for vector systems in the Euclidean plane.
The cones associated to some tranversal polymatroids.
The connected forcing connected vertex detour number of a graph
For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdₓ(G). For a minimum connected x-detour set Sₓ of G, a subset T ⊆ Sₓ is called a connected x-forcing subset...
The Connectivity Of Domination Dot-Critical Graphs With No Critical Vertices
An edge of a graph is called dot-critical if its contraction decreases the domination number. A graph is said to be dot-critical if all of its edges are dot-critical. A vertex of a graph is called critical if its deletion decreases the domination number. In A note on the domination dot-critical graphs, Discrete Appl. Math. 157 (2009) 3743-3745, Chen and Shiu constructed for each even integer k ≥ 4 infinitely many k-dot-critical graphs G with no critical vertices and k(G) = 1. In this paper, we refine...
The Connell sum sequence.
The construction of orthogonal k-skeins and latin k-cubes.
The construction of resolvable block-systems
The contractible subgraph of -connected graphs
An edge of a -connected graph is said to be -removable if is still -connected. A subgraph of a -connected graph is said to be -contractible if its contraction results still in a -connected graph. A -connected graph with neither removable edge nor contractible subgraph is said to be minor minimally -connected. In this paper, we show that there is a contractible subgraph in a -connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex of minor...
The contributions of Hilbert and Dehn to non-archimedean geometries and their impact on the italian school
In this paper we investigate the contribution of Dehn to the development of non-Archimedean geometries. We will see that it is possible to construct some models of non-Archimedean geometries in order to prove the independence of the continuity axiom and we will study the interrelations between Archimedes’ axiom and Legendre’s theorems. Some of these interrelations were also studied by Bonola, who was one of the very few Italian scholars to appreciate Dehn’s work. We will see that, if Archimedes’...
The converse of Kelly’s lemma and control-classes in graph reconstruction
We prove a converse of the well-known Kelly’s Lemma. This motivates the introduction of the general notions of -table, -congruence and control-class.
The convexity graph of minimal total dominating functions of a graph
The cost chromatic number and hypergraph parameters
In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
The cover pebbling theorem.
The cover time of deterministic random walks.
The cover-index of infinite graphs.