Graphs with edge-preserving majority functions
Discrete Mathematics
Closure properties of constraints
Journal of the ACM (JACM)
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
Closure Functions and Width 1 Problems
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
A polynomial-time algorithm for near-unanimity graphs
Journal of Algorithms
Near-Unanimity Functions and Varieties of Reflexive Graphs
SIAM Journal on Discrete Mathematics
Two new homomorphism dualities and lattice operations*
Journal of Logic and Computation
Hi-index | 0.00 |
We investigate the class of reflexive graphs that admit semilattice polymorphisms, and in doing so, give an algebraic characterisation of chordal graphs. In particular, we show that a graph G is chordal if and only if it has a semilattice polymorphism such that G is a subgraph of the comparability graph of the semilattice. Further, we find a new characterisation of the leafage of a chordal graph in terms of the width of the semilattice polymorphisms it admits. Finally, we introduce obstructions to various types of semilattice polymorphisms, and in doing so, show that the class of reflexive graphs admitting semilattice polymorphisms is not a variety. These are, to our knowledge, the first structural results on graphs with semilattice polymorphisms, beyond the conservative realm.