MathDB

Find the largest positive integer

k{}

for which there exists a convex polyhedron

\mathcal{P}

with 2022 edges, which satisfies the following properties:
[*]The degrees of the vertices of

\mathcal{P}

don’t differ by more than one, and [*]It is possible to colour the edges of

\mathcal{P}

with

k{}

colours such that for every colour

c{}

, and every pair of vertices

(v_1, v_2)

\mathcal{P}

, there is a monochromatic path between

v_1

and

v_2

in the colour

c{}

.
Viktor Simjanoski, Macedonia

Problem Statement