DeepAI AI Chat
Log In Sign Up

Polyhedral study of the Convex Recoloring problem

by   Manoel Campêlo, et al.
Universidade Federal de Minas Gerais
UFC informa

A coloring of the vertices of a connected graph is convex if each color class induces a connected subgraph. We address the convex recoloring (CR) problem defined as follows. Given a graph G and a coloring of its vertices, recolor a minimum number of vertices of G so that the resulting coloring is convex. This problem, known to be NP-hard even on paths, was firstly motivated by applications on perfect phylogenies. In this work, we study CR on general graphs from a polyhedral point of view. First, we introduce a full-dimensional polytope based on the idea of connected subgraphs, and present a class of valid inequalities with righthand side one that comprises all facet-defining inequalities with binary coefficients when the input graph is a tree. Moreover, we define a general class of inequalities with righthand side in {1, ..., k}, where k is the amount of colors used in the initial coloring, and show sufficient conditions for validity and facetness of such inequalities. Finally, we report on computational experiments for an application on mobile networks that can be modeled by the polytope of CR on paths. We evaluate the potential of the proposed inequalities to reduce the integrality gaps.


page 1

page 2

page 3

page 4


Total Coloring and Total Matching: Polyhedra and Facets

A total coloring of a graph G = (V, E) is an assignment of colors to ver...

An Exact Cutting Plane Algorithm to Solve the Selective Graph Coloring Problem in Perfect Graphs

Graph coloring is the problem of assigning a minimum number of colors to...

Graph multicoloring reduction methods and application to McDiarmid-Reed's Conjecture

A (a,b)-coloring of a graph G associates to each vertex a set of b color...

New bounds and constructions for neighbor-locating colorings of graphs

A proper k-coloring of a graph G is a neighbor-locating k-coloring if fo...

On List k-Coloring Convex Bipartite Graphs

List k-Coloring (Li k-Col) is the decision problem asking if a given gra...

Polyhedral Properties of the Induced Cluster Subgraphs

A cluster graph is a graph whose every connected component is a complete...

On the Dominant of the Multicut Polytope

Given a graph G=(V,E) and a set S ⊆V2 of terminal pairs, the minimum mul...