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Graph Theory

3-Decomposition Conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   (3-Decomposition Conjecture) Every connected cubic graph $ G $ has a decomposition into a spanning tree, a family of cycles and a matching.

Keywords: cubic graph

Posted by arthur
updated January 24th, 2017
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Graph Theory » Basic G.T.

Domination in cubic graphs ★★

Author(s): Reed

Problem   Does every 3-connected cubic graph $ G $ satisfy $ \gamma(G) \le \lceil |G|/3 \rceil $ ?

Keywords: cubic graph; domination

Posted by mdevos
updated August 19th, 2009
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Graph Theory » Coloring » Edge coloring

Universal Steiner triple systems ★★

Author(s): Grannell; Griggs; Knor; Skoviera

Problem   Which Steiner triple systems are universal?

Keywords: cubic graph; Steiner triple system

Posted by macajova
updated October 5th, 2007
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