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JCT
2010
102views more  JCT 2010»
15 years 29 days ago
Coloring axis-parallel rectangles
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by prec...
János Pach, Gábor Tardos
JGT
2010
113views more  JGT 2010»
15 years 29 days ago
Coloring plane graphs with independent crossings
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...
Daniel Král', Ladislav Stacho
DMTCS
2010
123views Mathematics» more  DMTCS 2010»
14 years 12 months ago
A characterization of infinite smooth Lyndon words
In a recent paper, Brlek, Jamet and Paquin showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: are they the only...
Geneviève Paquin
89
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DM
2011
184views Education» more  DM 2011»
14 years 9 months ago
Graphs of arbitrary excessive class
We show that there exists a family of r-regular graphs of arbitrarily large excessive index for each integer r greater than 3. Furthermore, we answer a question in [1] showing tha...
Giuseppe Mazzuoccolo, M. Young
JAT
2011
64views more  JAT 2011»
14 years 9 months ago
Two remarks on remotality
We prove that there exists a weakly closed and bounded subset E of c0 which is not remotal from 0, and such that co (E) is remotal from 0. This answers a question of M. Mart´ın ...
Michal Kraus