Let $\mathcal F$ be a hypergraph with the property that for any two edges $F_1, F_2 \in \mathcal F, |F_1 ∩ F_2 | ≥ 2$. Prove that $\mathcal F$ is two-colourable.
I have no idea to prove the claim. Can anyone give me some hints?
Hypergraph with the property that for any two edges $F_1, F_2 \in \mathcal F, |F_1 ∩ F_2 | ≥ 2$ is 2-colourable
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graph-theory
coloring
hypergraphs
1 Answers
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This is problem 33 in chapter "§13 Hypergraphs" in the book "Combinatorial Problems and Exercises" by László Lovász:
We construct the 2-colouring (black, white) of the vertex set $V=\{v_1,...,v_n\}$ step by step. Assume that the points $v_1,...,v_i$ have already been coloured ($i