Complexity classification of the edge coloring problem for a family of graph classes
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Dmitriy S. Malyshev
Abstract
A class of graphs is called monotone if it is closed under deletion of vertices and edges. Any such class may be defined in terms of forbidden subgraphs. The chromatic index of a graph is the smallest number of colors required for its edge-coloring such that any two adjacent edges have different colors. We obtain a complete classification of the complexity of the chromatic index problem for all monotone classes defined in terms of forbidden subgraphs having at most 6 edges or at most 7 vertices.
Originally published in Diskretnaya Matematika (2016) 28, №2, 44–50 (in Russian).
Acknowledgment
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-31-60008-mol_a_dk, the Council on Grants of the President of the Russian Federation (grant no. MK-4819.2016.1), and the LATNA laboratory at the National Research University Higher School of Economics.
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Articles in the same Issue
- Frontmatter
- Extension of the Rissanen algorithm to the factorization of block-Hankel matrices for solving systems of linear equations
- On asymptotics of branching processes with immigration
- On some measures of complexity of finite Abelian groups
- Complexity classification of the edge coloring problem for a family of graph classes
- On FE-precomplete classes in countable-valued logic
- On 1-stable perfectly balanced Boolean functions
- On bases of closed classes of vector functions of many-valued logic
- On the asymptotic normality of some sums of dependent random variables
- On serial rings
Articles in the same Issue
- Frontmatter
- Extension of the Rissanen algorithm to the factorization of block-Hankel matrices for solving systems of linear equations
- On asymptotics of branching processes with immigration
- On some measures of complexity of finite Abelian groups
- Complexity classification of the edge coloring problem for a family of graph classes
- On FE-precomplete classes in countable-valued logic
- On 1-stable perfectly balanced Boolean functions
- On bases of closed classes of vector functions of many-valued logic
- On the asymptotic normality of some sums of dependent random variables
- On serial rings
