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Part of 2018 Miklós Schweitzer

Problems(1)

Chromatic number is countable

Source: Mikl&oacute;s Schweitzer 2018 P1

S\subset \mathbb{R}

be a closed set and

f:\mathbb{R}^{2n}\to \mathbb{R}

be a continuous function. Define a graph

G

as follows: Let

x

G

x\in \mathbb{R}^{n}

f(x,x)\not\in S

, then connect the vertices

x

y

G

f(x,y)\in S

f(y,x)\in S

. Show that the chromatic number of

G

college contestscountability