Determining the total colouring number is NP-hard
Discrete Mathematics
List edge and list total colourings of multigraphs
Journal of Combinatorial Theory Series B
On list edge-colorings of subcubic graphs
Discrete Mathematics
Efficient algorithms for Petersen's matching theorem
Journal of Algorithms
Optimal randomized EREW PRAM algorithms for finding spanning forests
Journal of Algorithms
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
4-edge-coloring graphs of maximum degree 3 in linear time
Information Processing Letters
Delta-List Vertex Coloring in Linear Time
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
List Total Colourings of Graphs
Combinatorics, Probability and Computing
Graph Theory With Applications
Graph Theory With Applications
| Hi-index | 0.00 |
We present efficient algorithms for three coloring problems on subcubic graphs (ones with maximum degree 3). These algorithms are based on a simple decomposition principle for subcubic graphs. The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. As evidence we give the first randomized EREW PRAM algorithm that uses O(n/log n) processors and runs in O(log n) time with high probability, where n is the number of vertices of the input graph. The second algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The third algorithm generalizes this to the first linear-time algorithm to 5-list-total-color subcubic graphs.