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JCO
2007
130views more  JCO 2007»
10 years 1 months ago
On edge orienting methods for graph coloring
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
Bernard Gendron, Alain Hertz, Patrick St-Louis
ENDM
2007
68views more  ENDM 2007»
10 years 1 months ago
List Colouring Squares of Planar Graphs
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3
Frédéric Havet, Jan van den Heuvel, ...
ENDM
2007
111views more  ENDM 2007»
10 years 1 months ago
Claw-free circular-perfect graphs
The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs is a superclass of perfect graphs defined by means of this...
Arnaud Pêcher, Xuding Zhu
JCT
2006
73views more  JCT 2006»
10 years 1 months ago
Colouring lines in projective space
Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the kdimensional subspaces of V as its vertices, where two subspaces and are adjacent if and...
Ameera Chowdhury, Chris D. Godsil, Gordon F. Royle
JSYML
2008
100views more  JSYML 2008»
10 years 1 months ago
Measurable chromatic numbers
We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three...
Benjamin D. Miller
JGT
2008
103views more  JGT 2008»
10 years 1 months ago
Game coloring the Cartesian product of graphs
: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors....
Xuding Zhu
IPL
2008
145views more  IPL 2008»
10 years 1 months ago
Complexity analysis of a decentralised graph colouring algorithm
Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which descisions are made locally with no information about the graph�...
Ken R. Duffy, N. O'Connell, Artëm Sapozhnikov
EJC
2006
10 years 1 months ago
Symplectic graphs and their automorphisms
The general symplectic graph Sp(2, q) is introduced. It is shown that Sp(2, q) is strongly regular. Its parameters are computed, its chromatic number and group of graph automorphis...
Zhongming Tang, Zhe-xian Wan
DM
2006
79views more  DM 2006»
10 years 1 months ago
Conditional colorings of graphs
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
Hong-Jian Lai, Jianliang Lin, Bruce Montgomery, Ta...
COMBINATORICS
2006
123views more  COMBINATORICS 2006»
10 years 1 months ago
The Non-Crossing Graph
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....
Nathan Linial, Michael E. Saks, David Statter
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