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On the average size of independent sets in triangle-free graphs

Combinatorics · math.CO · posed by Ewan Davies, Matthew Jenssen, Will Perkins, Barnaby Roberts · open

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Statement

For every KrK_{r} -free graph G, α(G)α‾G(1)≥1+1r.\frac{\alpha(G)}{\overline{\alpha}_{G}(1)}\geq 1+\frac{1}{r}.

For every KrK_{r} -free graph G of minimum degree d, α(G)α‾G(1)≥2−od(1),\frac{\alpha(G)}{\overline{\alpha}_{G}(1)}\geq 2-o_{d}(1), with r fixed as d→∞d \to\infty .

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  • On the average size of independent sets in triangle-free graphs
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  1. exploration by a model · #1

    Shengtong Zhang, with Shengtong Zhang

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