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DM
2008
116views more  DM 2008»
13 years 9 months ago
Total and fractional total colourings of circulant graphs
In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional ...
Riadh Khennoufa, Olivier Togni
LICS
2010
IEEE
13 years 6 months ago
Fixed-Point Definability and Polynomial Time on Graphs with Excluded Minors
We prove that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. That is, for every class C of graphs such that some graph H is...
Martin Grohe
JCT
2011
115views more  JCT 2011»
13 years 4 months ago
Sharp thresholds for hypergraph regressive Ramsey numbers
The f-regressive Ramsey number Rreg f (d, n) is the minimum N such that every colouring of the d-tuples of an N-element set mapping each x1, . . . , xd to a colour ≤ f(x1) contai...
Lorenzo Carlucci, Gyesik Lee, Andreas Weiermann
COCOON
2006
Springer
14 years 22 days ago
Optimal Acyclic Edge Colouring of Grid Like Graphs
We determine the values of the acyclic chromatic index of a class of graphs referred to as d-dimensional partial tori. These are graphs which can be expressed as the cartesian prod...
Rahul Muthu, N. Narayanan, C. R. Subramanian
TPHOL
2002
IEEE
14 years 1 months ago
The 5 Colour Theorem in Isabelle/Isar
Based on an inductive definition of triangulations, a theory of undirected planar graphs is developed in Isabelle/HOL. The proof of the 5 colour theorem is discussed in some detai...
Gertrud Bauer, Tobias Nipkow