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10-colorable graph

Source: Indian Team Selection Test 2015 Day 2 Problem 3

July 11, 2015
graph theorycombinatorics

Problem Statement

Let GG be a simple graph on the infinite vertex set V={v1,v2,v3,…}V=\{v_1, v_2, v_3,\ldots\}. Suppose every subgraph of GG on a finite vertex subset is 1010-colorable, Prove that GG itself is 1010-colorable.
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