Let G H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominating the Cartesian product of a graph and K2, Discuss. Math. Graph Theory 24(3) (2004), 389–402] characterized prism fixers, i.e., graphs G for which γ(G K2) = γ(G), and noted that γ(G Kn) ≥ min{|V (G)|, γ(G)+n−2}. We call a graph G a consistent fixer if γ(G Kn) = γ(G)+n−2 for each n such that 2 ≤ n...

We call a graph matching-covered if every line belongs to a perfect matching. We study the technique of "ear-decompositions" of such graphs. We prove that a non-bipartite matchingcovered graph contains K~ or K2@Ka (the triangular prism). Using this result, we give new characterizations of those graphs whose matching and covering numbers are equal. We apply these results to the theory of r-criti...

The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex in all the other color classes. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 4. The exceptions are the Petersen graph, K3,3, the prism over K3, and one more sporadic example on 10 ...

For each proper subgraph H of K5, we determine all pairs (k, d) such that every H-minor-free graph is (k, d)-choosable or (k, d)-choosable. The main structural lemma is that the only 3-connected (K5 − e)-minor-free graphs are wheels, the triangular prism, and K3,3; this is used to prove that every (K5 − e)-minor-free graph is 4-choosable and (3, 1)-choosable.

We report in this paper on our results of modeling and analyzing with the probabilistic model checker PRISM the energy efficiency of various cluster scheduling schemes. These schemes were originally introduced by Do, Vu, Tran, and Nguyen in their paper “A generalized model for investigating scheduling schemes in computational clusters” and analyzed by simulation there. Our investigations with P...

42 An understanding of the transfer (or generalization) of motor adaptations between legs and 43 across tasks during walking has remained elusive due to limited research and mixed results. Here, 44 we asked whether stepping sequences or task constraints introduced during walking prism 45 adaptation tasks influence generalization patterns. Forty subjects adapted to prism glasses in 46 precision ...