On the Widom–Rowlinson Occupancy Fraction in Regular Graphs

COMBINATORICS PROBABILITY & COMPUTING, pp. 183-194, 2017.

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Abstract:

We consider the Widom-Rowlinson model of two types of interacting particles on d-regular graphs. We prove a tight upper bound on the occupancy fraction, the expected fraction of vertices occupied by a particle under a random configuration from the model. The upper bound is achieved uniquely by unions of complete graphs on d + 1 vertices, ...More

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