Let Bk be the bipartite graph defined by the subsets of {1, . . . , 2k + 1} of size k and k + 1. We prove that the prism over Bk is hamiltonian. We also show that Bk has a closed spanning 2-trail.

We show that for every 3-connected cubic graph G, the prism G×K2 has cycles of every even length. Furthermore, if G has a triangle, then G × K2 is pancyclic.

In this paper we determine completely the class of binary matroids with no minors isomor-phic to the cycle matroid of the prism graph M*(Ks\e), its dual M(Ks\e), and the binary affine cube AG(3, 2).

An edge in a k-connected graph G is called k-contractible if the graph G/e obtained from G by contracting e is k-connected. Generalizing earlier results on 3-contractible edges in spanning trees of 3-connected graphs, we prove that (except for the graphs Kk+1 if k ∈ {1, 2}) (a) every spanning tree of a k-connected triangle free graph has two k-contractible edges, (b) every spanning tree of a k-...

We investigate the well-known problem of counting graph imbeddings on all oriented surfaces with a focus on graphs that are obtained by pasting together two root-edges of another base graph. We require that the partitioned genus distribution of the base graph with respect to these root-edges be known and that both root-edges have two 2-valent endpoints. We derive general formulas for calculatin...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

CSL is a stochastic temporal logic that has been defined for continuous time Markov chains, and that allows the checking of whether a single state, or a set of states, satisfies a given probabilistic condition defined over states or over a path of states. In this paper we consider the problem of CSL model checking in the context of Generalized Stochastic Petri Nets. We present a translation fro...

Let β(G) and Γ(G) be the independence number and the upper domination number of a graphG, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs, absorbantly perfect graphs, and circular arc graphs. In this article, we present a characterization of Γ-per...

For a given approximate vertex coloring algorithm a graph is said to be slightly hard-tocolor (SHC) if some implementation of the algorithm uses more colors than the minimum needed. Similarly, a graph is said to be hard-to-color (HC) if every implementation of the algorithm results in a nonoptimal coloring. We study smallest such graphs for the smallest-last (SL) coloring algorithm. Our main re...

We prove that every 3-connected 2-indivisible infinite planar graph has a 1-way infinite 2-walk. (A graph is 2-indivisible if deleting finitely many vertices leaves at most one infinite component, and a 2-walk is a spanning walk using every vertex at most twice.) This improves a result of Timar, which assumed local finiteness. Our proofs use Tutte subgraphs, and allow us to also provide other r...