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Graph Theory » Topological G.T. » Coloring

5-local-tensions ★★

Author(s): DeVos

Conjecture   There exists a fixed constant $ c $ (probably $ c=4 $ suffices) so that every embedded (loopless) graph with edge-width $ \ge c $ has a 5-local-tension.

Keywords: coloring; surface; tension

Posted by mdevos
updated June 22nd, 2007
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Graph Theory » Topological G.T. » Crossing numbers

Drawing disconnected graphs on surfaces ★★

Author(s): DeVos; Mohar; Samal

Conjecture   Let $ G $ be the disjoint union of the graphs $ G_1 $ and $ G_2 $ and let $ \Sigma $ be a surface. Is it true that every optimal drawing of $ G $ on $ \Sigma $ has the property that $ G_1 $ and $ G_2 $ are disjoint?

Keywords: crossing number; surface

Posted by mdevos
updated September 30th, 2007
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Graph Theory » Topological G.T. » Coloring

Grunbaum's Conjecture ★★★

Author(s): Grunbaum

Conjecture   If $ G $ is a simple loopless triangulation of an orientable surface, then the dual of $ G $ is 3-edge-colorable.

Keywords: coloring; surface

Posted by mdevos
updated March 23rd, 2009
5 comments
Graph Theory » Topological G.T. » Genus

Consecutive non-orientable embedding obstructions ★★★

Author(s):

Conjecture   Is there a graph $ G $ that is a minor-minimal obstruction for two non-orientable surfaces?

Keywords: minor; surface

Posted by Bruce Richter
updated September 15th, 2010
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