Displaying similar documents to “Flows on the join of two graphs”

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...

Join of two graphs admits a nowhere-zero 3 -flow

Saieed Akbari, Maryam Aliakbarpour, Naryam Ghanbari, Emisa Nategh, Hossein Shahmohamad (2014)

Czechoslovak Mathematical Journal

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Let G be a graph, and λ the smallest integer for which G has a nowhere-zero λ -flow, i.e., an integer λ for which G admits a nowhere-zero λ -flow, but it does not admit a ( λ - 1 ) -flow. We denote the minimum flow number of G by Λ ( G ) . In this paper we show that if G and H are two arbitrary graphs and G has no isolated vertex, then Λ ( G ∨ H ) ≤ 3 except two cases: (i) One of the graphs G and H is K 2 and the other is 1 -regular. (ii) H = K 1 and G is a graph with at least one isolated vertex or a component whose every...

The graph polynomial and the number of proper vertex coloring

Michael Tarsi (1999)

Annales de l'institut Fourier

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Alon and Tarsi presented in a previous paper a certain weighted sum over the set of all proper k -colorings of a graph, which can be computed from its graph polynomial. The subject of this paper is another combinatorial interpretation of the same quantity, expressed in terms of the numbers of certain modulo k flows in the graph. Some relations between graph parameters can be obtained by combining these two formulas. For example: The number of proper 3-colorings of a 4-regular graph and...