Connected and Loosely Connected List Homomorphisms

Authors:
Narayan Vikas
Affiliations:
-
Venue:
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Year:
2002

Citing 11
Cited 1

The complexity of some polynomial network consistency algorithms for constraint satisfaction problems

Artificial Intelligence
Absolute retracts of bipartite graphs

Discrete Applied Mathematics
On the complexity of H-coloring

Journal of Combinatorial Theory Series B
Polynomial graph-colorings

Discrete Applied Mathematics
Absolute reflexive retracts and absolute bipartite retracts

Discrete Applied Mathematics
List homomorphisms to reflexive graphs

Journal of Combinatorial Theory Series B
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

SIAM Journal on Computing
Graph classes: a survey

Graph classes: a survey
Computational complexity of compaction to cycles

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computational Complexity of Compaction to Reflexive Cycles

SIAM Journal on Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithms for partition of some class of graphs under compaction

COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study a special graph colouring problem, called the list homomorphism problem, which is a generalisation of the list colouring problem. Several variants of the list homomorphism problem have been considered before. In particular, a complete complexity classification of the connected list homomorphism problem for reflexive graphs has been given before, according to which the problem is polynomial time solvable for reflexive chordal graphs, and NP-complete for reflexive non-chordal graphs. A natural analogue of this result is known not to hold for this problem for bipartite graphs. We observe that the notion of list connectivity in the problem needs to be modified for bipartite graphs. We introduce a new variant called the bipartite loosely connected list homomorphism problem for bipartite graphs. We give a complete complexity classification of this problem, showing that it is polynomial time solvable for chordal bipartite graphs, and NP-complete for non-chordal bipartite graphs. This result is analogous to the result for the connected list homomorphism problem for reflexive graphs. We present a linear time algorithm for the bipartite loosely connected list homomorphism problem for chordal bipartite graphs, as well as for the connected list homomorphism problem for reflexive chordal graphs, showing that the algorithms can decide just by testing whether or not the corresponding consistency tests succeed.