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McDiarmid, Colin
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.
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Keywords: maximum clique; Partitioning
Arc-disjoint directed cycles in regular directed graphs ★★
Author(s): Alon; McDiarmid; Molloy
Conjecture If
is a
-regular directed graph with no parallel arcs, then
contains a collection of
arc-disjoint directed cycles.
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Keywords:
Weighted colouring of hexagonal graphs. ★★
Conjecture There is an absolute constant
such that for every hexagonal graph
and vertex weighting
,
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Keywords:
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