TY - GEN

T1 - Counting H-colorings of partial k-trees

AU - Dìaz, Josep

AU - Serna, Maria

AU - Thilikos, Dimitrios M.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

PY - 2001

Y1 - 2001

N2 - The problem of counting all H-colorings of a graph G of n vertices is considered. While the problem is, in general, #P-complete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a k-tree or, in the case where G is directed, when the underlying graph of G is a k-tree. Our algorithms remain polynomial even in the case where k = O(log n) or in the case where the size of H is O(n). Our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k-trees such as core checking and chromatic polynomial computation.

AB - The problem of counting all H-colorings of a graph G of n vertices is considered. While the problem is, in general, #P-complete, we give linear time algorithms that solve the main variants of this problem when the input graph G is a k-tree or, in the case where G is directed, when the underlying graph of G is a k-tree. Our algorithms remain polynomial even in the case where k = O(log n) or in the case where the size of H is O(n). Our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k-trees such as core checking and chromatic polynomial computation.

UR - http://www.scopus.com/inward/record.url?scp=84944145309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944145309&partnerID=8YFLogxK

U2 - 10.1007/3-540-44679-6_33

DO - 10.1007/3-540-44679-6_33

M3 - Conference contribution

AN - SCOPUS:84944145309

SN - 9783540424949

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 298

EP - 307

BT - Computing and Combinatorics - 7th Annual International Conference, COCOON 2001, Proceedings

A2 - Wang, Jie

PB - Springer Verlag

T2 - 7th Annual International Conference on Computing and Combinatorics, COCOON 2001

Y2 - 20 August 2001 through 23 August 2001

ER -