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» Colouring Vertices of Triangle-Free Graphs
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93
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STOC
2009
ACM
152views Algorithms» more  STOC 2009»
15 years 6 months ago
Green's conjecture and testing linear-invariant properties
A system of linear equations in p unknowns Mx = b is said to have the removal property if every set S ⊆ {1, . . . , n} which contains o(np− ) solutions of Mx = b can be turned...
Asaf Shapira
81
Voted
DM
2010
108views more  DM 2010»
14 years 11 months ago
Grundy number and products of graphs
The Grundy number of a graph G, denoted by (G), is the largest k such that G has a greedy k-colouring, that is a colouring with k colours obtained by applying the greedy algorithm...
Marie Asté, Frédéric Havet, C...
86
Voted
JGT
2007
87views more  JGT 2007»
14 years 11 months ago
A new upper bound on the cyclic chromatic number
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring...
Oleg V. Borodin, Hajo Broersma, Alexei N. Glebov, ...
87
Voted
DM
2010
118views more  DM 2010»
14 years 11 months ago
Discrepancy and signed domination in graphs and hypergraphs
For a graph G, a signed domination function of G is a two-colouring of the vertices of G with colours +1 and
Anush Poghosyan, Vadim E. Zverovich
82
Voted
WDAG
2000
Springer
112views Algorithms» more  WDAG 2000»
15 years 3 months ago
More Lower Bounds for Weak Sense of Direction: The Case of Regular Graphs
A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
Paolo Boldi, Sebastiano Vigna