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Borodin, Oleg V.


Graph Theory » Coloring

List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

Conjecture   If $ G $ is the total graph of a multigraph, then $ \chi_\ell(G)=\chi(G) $.

Keywords: list coloring; Total coloring; total graphs

Posted by Jon Noel
updated August 29th, 2013
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Graph Theory » Coloring » Vertex coloring

Acyclic list colouring of planar graphs. ★★★

Author(s): Borodin; Fon-Der-Flasss; Kostochka; Raspaud; Sopena

Conjecture   Every planar graph is acyclically 5-choosable.

Keywords:

Posted by fhavet
updated March 7th, 2013
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Graph Theory

The Borodin-Kostochka Conjecture ★★

Author(s): Borodin; Kostochka

Conjecture   Every graph with maximum degree $ \Delta \geq 9 $ has chromatic number at most $ \max\{\Delta-1, \omega\} $.

Keywords:

Posted by Andrew King
updated September 10th, 2012
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Graph Theory » Topological G.T. » Coloring

Degenerate colorings of planar graphs ★★★

Author(s): Borodin

A graph $ G $ is $ k $-degenerate if every subgraph of $ G $ has a vertex of degree $ \le k $.

Conjecture   Every simple planar graph has a 5-coloring so that for $ 1 \le k \le 4 $, the union of any $ k $ color classes induces a $ (k-1) $-degenerate graph.

Keywords: coloring; degenerate; planar

Posted by mdevos
updated May 21st, 2008
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