Displaying similar documents to “A graphic generalization of arithmetic.”

Flows on the join of two graphs

Robert Lukoťka, Edita Rollová (2013)

Mathematica Bohemica

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The join of two graphs G and H is a graph formed from disjoint copies of G and H by connecting each vertex of G to each vertex of H . We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero 3 -flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus...

Exploiting the structure of conflict graphs in high level synthesis

Klaus Jansen (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we analyze the computational complexity of a processor optimization problem. Given operations with interval times in a branching flow graph, the problem is to find an assignment of the operations to a minimum number of processors. We analyze the complexity of this assignment problem for flow graphs with a constant number of program traces and a constant number of processors.

Antisymmetric flows and strong colourings of oriented graphs

J. Nešetřill, André Raspaud (1999)

Annales de l'institut Fourier

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The homomorphisms of oriented or undirected graphs, the oriented chromatic number, the relationship between acyclic colouring number and oriented chromatic number, have been recently intensely studied. For the purpose of duality, we define the notions of strong-oriented colouring and antisymmetric-flow. An antisymmetric-flow is a flow with values in an additive abelian group which uses no opposite elements of the group. We prove that the strong-oriented chromatic number χ → s (as the modular...