Number Theory » Analytic N.T.

Euler-Mascheroni constant ★★★

Author(s):

Question   Is Euler-Mascheroni constant an transcendental number?

Keywords: constant; Euler; irrational; Mascheroni; rational; transcendental

Posted by Juggernaut
updated January 21st, 2013
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Geometry

Covering a square with unit squares ★★

Author(s):

Conjecture   For any integer $ n \geq 1 $, it is impossible to cover a square of side greater than $ n $ with $ n^2+1 $ unit squares.

Keywords:

Posted by Martin Erickson
updated August 1st, 2011
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Graph Theory

Covering powers of cycles with equivalence subgraphs ★

Author(s):

Conjecture   Given $ k $ and $ n $, the graph $ C_{n}^k $ has equivalence covering number $ \Omega(k) $.

Keywords:

Posted by Andrew King
updated July 7th, 2011
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Graph Theory » Coloring » Labeling

Good Edge Labelings ★★

Author(s): Araújo; Cohen; Giroire; Havet

Question   What is the maximum edge density of a graph which has a good edge labeling?

We say that a graph is good-edge-labeling critical, if it has no good edge labeling, but every proper subgraph has a good edge labeling.

Conjecture   For every $ c<4 $, there is only a finite number of good-edge-labeling critical graphs with average degree less than $ c $.

Keywords: good edge labeling, edge labeling

Posted by DOT
updated February 16th, 2013
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