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2018

On a fractional version of Haemers' bound

Bukh, Boris, Cox, Christopher

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In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak.

This bound is a common strengthening of both Haemers' bound and the fractional chromatic number of a graph.
We show that this fractional version outperforms any bound on the Shannon capacity that could be attained through Haemers' bound.
We show also that this bound is multiplicative, unlike Haemers' bound.

On a fractional version of Haemers' bound · Around

Built on

The zero error capacity of a noisy channel
C. Shannon · 1956
Earlier work this paper cites.
On some problems of Lovász concerning the Shannon capacity of a graph
W. Haemers · 1979
Earlier work this paper cites.
On the Shannon capacity of a graph
L. Lovász · 1979
Earlier work this paper cites.

Similar

An upper bound for the Shannon capacity of a graph
W. Haemers · 1981
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Association schemes and the Shannon capacity: Eberlein-polynomials and the Erdős–Ko–Rado theorem
A. Schrijver · 1981
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The Shannon capacity of a union
N. Alon · 1998
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Then

A graph-theoretic approach to network coding
A. Blasiak · 2013
Later among the works it cites.
A bound on the Shannon capacity via a linear programming variation
Original
S. Hu, I. Tamo, and O. Shayevitz · 2018
Closest in time.

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