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110
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DM
2010
83views more  DM 2010»
15 years 1 months ago
Polychromatic colorings of arbitrary rectangular partitions
A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex colorings using four colors o...
Dániel Gerbner, Balázs Keszegh, Nath...
JCT
2006
80views more  JCT 2006»
15 years 1 months ago
Extending precolorings to circular colorings
Fix positive integers k , d , k, d such that k /d > k/d 2. If P is a set of vertices in a (k, d)-colorable graph G, and any two vertices of P are separated by distance at leas...
Michael O. Albertson, Douglas B. West
110
Voted
APPROX
2004
Springer
149views Algorithms» more  APPROX 2004»
15 years 7 months ago
Edge Coloring with Delays
Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on o...
Noga Alon, Vera Asodi
104
Voted
ENDM
2007
96views more  ENDM 2007»
15 years 1 months ago
Sub-Ramsey Numbers for Arithmetic Progressions and Schur Triples
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
Jacob Fox, Veselin Jungic, Rados Radoicic
114
Voted
SIAMDM
2008
97views more  SIAMDM 2008»
15 years 1 months ago
Disjoint Color-Avoiding Triangles
A set of pairwise edge-disjoint triangles of an edge-colored Kn is r-color avoiding if it does not contain r monochromatic triangles, each having a different color. Let fr(n) be th...
Raphael Yuster