DeepAI AI Chat
Log In Sign Up

On List k-Coloring Convex Bipartite Graphs

by   Josep Diaz, et al.
Kadir Has University
Universitat Politècnica de Catalunya

List k-Coloring (Li k-Col) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in 1,2,..,k. The problem is known to be NP-hard even for k=3 within the class of 3-regular planar bipartite graphs and for k=4 within the class of chordal bipartite graphs. In 2015, Huang, Johnson and Paulusma asked for the complexity of Li 3-Col in the class of chordal bipartite graphs. In this paper we give a partial answer to this question by showing that Li k-Col is polynomial in the class of convex bipartite graphs. We show first that biconvex bipartite graphs admit a multichain ordering, extending the classes of graphs where a polynomial algorithm of Enright, Stewart and Tardos (2014) can be applied to the problem. We provide a dynamic programming algorithm to solve the Li k-Col in the calss of convex bipartite graphs. Finally we show how our algorithm can be modified to solve the more general Li H-Col problem on convex bipartite graphs.


page 1

page 2

page 3

page 4


List 3-Coloring on Comb-Convex and Caterpillar-Convex Bipartite Graphs

Given a graph G=(V, E) and a list of available colors L(v) for each vert...

Role Coloring Bipartite Graphs

A k-role coloring alpha of a graph G is an assignment of k colors to the...

More Effective Randomized Search Heuristics for Graph Coloring Through Dynamic Optimization

Dynamic optimization problems have gained significant attention in evolu...

Coloring Problems on Bipartite Graphs of Small Diameter

We investigate a number of coloring problems restricted to bipartite gra...

Distance-Two Colorings of Barnette Graphs

Barnette identified two interesting classes of cubic polyhedral graphs f...

Approximating Bin Packing with Conflict Graphs via Maximization Techniques

We give a comprehensive study of bin packing with conflicts (BPC). The i...

Min orderings and list homomorphism dichotomies for signed and unsigned graphs

The CSP dichotomy conjecture has been recently established, but a number...