![](/files/happy5.png)
maximum clique
2-colouring a graph without a monochromatic maximum clique ★★
Conjecture If
is a non-empty graph containing no induced odd cycle of length at least
, then there is a
-vertex colouring of
in which no maximum clique is monochromatic.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ 5 $](/files/tex/87f5fe1d4b06035debb52cf2d67802fbfa9cb4ab.png)
![$ 2 $](/files/tex/5271e36bb1c040e0f14061d89cd97d0c86d4e06f.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: maximum clique; Partitioning
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