Search results for: SIGNED GRAPHS

• Edge coloring of graphs of signed class 1 and 2

  Publication

  • R. Janczewski
  • K. Turowski
  • B. Wróblewski

  - DISCRETE APPLIED MATHEMATICS - Year 2023

  Recently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...

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• Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

  Publication

  • M. Rosicka
  • R. Ramanathan
  • P. Gnaciński
  • K. Horodecki
  • M. Horodecki
  • P. Horodecki
  • S. Severini

  - NEW JOURNAL OF PHYSICS - Year 2016

  We study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the...

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