New Formulation for Coloring Circle Graphs and its Application to Capacitated Stowage Stack Minimization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866908555950424064 |
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| author | Tanaka, Masato Matsui, Tomomi |
| author_facet | Tanaka, Masato Matsui, Tomomi |
| contents | A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we propose a new integer linear programming formulation for a coloring problem on circle graphs. We also show that the linear relaxation problem of our formulation finds the fractional chromatic number of a given circle graph. As a byproduct, our formulation gives a polynomial-sized linear programming formulation for calculating the fractional chromatic number of a circle graph. We also extend our result to a formulation for a capacitated stowage stack minimization problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_00691 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | New Formulation for Coloring Circle Graphs and its Application to Capacitated Stowage Stack Minimization Tanaka, Masato Matsui, Tomomi Discrete Mathematics 05C15, 90C10, 90C27, 90C35, 05C72 A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we propose a new integer linear programming formulation for a coloring problem on circle graphs. We also show that the linear relaxation problem of our formulation finds the fractional chromatic number of a given circle graph. As a byproduct, our formulation gives a polynomial-sized linear programming formulation for calculating the fractional chromatic number of a circle graph. We also extend our result to a formulation for a capacitated stowage stack minimization problem. |
| title | New Formulation for Coloring Circle Graphs and its Application to Capacitated Stowage Stack Minimization |
| topic | Discrete Mathematics 05C15, 90C10, 90C27, 90C35, 05C72 |
| url | https://arxiv.org/abs/2102.00691 |