Decomposing graphs into interval colorable subgraphs and no-wait multi-stage schedules
Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan

TL;DR
This paper introduces the concept of interval coloring thickness, a measure of how a graph can be decomposed into interval colorable subgraphs, with applications in scheduling and timetabling.
Contribution
It defines the new notion of interval coloring thickness and provides bounds and conditions for graphs to be decomposed into interval colorable subgraphs.
Findings
Connected 3-edge colorable graphs with max degree 3 are interval colorable.
Upper bounds on interval coloring thickness for general graphs.
Improved bounds for bipartite, planar, and complete multipartite graphs.
Abstract
A graph is called interval colorable if it has a proper edge coloring with colors such that the colors of the edges incident to every vertex of form an interval of integers. Not all graphs are interval colorable; in fact, quite few families have been proved to admit interval colorings. In this paper we introduce and investigate a new notion, the interval coloring thickness of a graph , denoted , which is the minimum number of interval colorable edge-disjoint subgraphs of whose union is . Our investigation is motivated by scheduling problems with compactness requirements, in particular, problems whose solution may consist of several schedules, but where each schedule must not contain any waiting periods or idle times for all involved parties. We first prove that every connected properly -edge colorable graph with maximum…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Optimization and Search Problems
