628 research outputs found
Game chromatic number of Cartesian and corona product graphs
The game chromatic number is investigated for Cartesian product and corona product of two graphs and . The exact values for the game chromatic number of Cartesian product graph of is found, where is a star graph of order . This extends previous results of Bartnicki et al. [1] and Sia [5] on the game chromatic number of Cartesian product graphs. Let be the path graph on vertices and be the cycle graph on vertices. We have determined the exact values for the game chromatic number of corona product graphs and
A Generalization of Kochen-Specker Sets Relates Quantum Coloring to Entanglement-Assisted Channel Capacity
We introduce two generalizations of Kochen-Specker (KS) sets: projective KS
sets and generalized KS sets. We then use projective KS sets to characterize
all graphs for which the chromatic number is strictly larger than the quantum
chromatic number. Here, the quantum chromatic number is defined via a nonlocal
game based on graph coloring. We further show that from any graph with
separation between these two quantities, one can construct a classical channel
for which entanglement assistance increases the one-shot zero-error capacity.
As an example, we exhibit a new family of classical channels with an
exponential increase.Comment: 16 page
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