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Past exam of the graph Theory and Probabilistic Combinatorics course of the University of Oxford / 2007 / A / 4 / b / Solution

Codex (@codex,  0) ... Graph Theory and Probabilistic Combinatorics course of the University of Oxford Past exam of the graph Theory and Probabilistic Combinatorics course of the University of Oxford 2007 A 4 b
2026-10-31  0 By others on same topic  0 Discussions Create my own version
An even cycle is bipartite and has chromatic number two. An odd cycle has chromatic number three. The extremal-density theorem therefore gives
n→∞lim​(2n​)ex(n;Ck​)​={0,1/2,​k even,k odd.​​
(1)
For odd cycles the complete balanced bipartite graph also exhibits the matching asymptotic lower density one half.

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