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Coloring graphs with forbidden induced subgraphs Chudnovsky, Maria
Description
The problem of testing if a graph can be colored with a given number $k$ of colors is NP-complete for every $k>2$. But what if we have more information about the input graph, namely that some fixed graph $H$ is not present in it as an induced subgraph? It is known that the problem remains NP-complete even for $k=3$, unless $H$ is the disjoint union of paths. We consider the following two questions: 1. For which graphs $H$ is there a polynomial time algorithm to 3-color (or in general $k$-color) an $H$-free graph? 2. For which graphs $H$ are there finitely many 4-critical $H$-free graphs? This talk will survey recent progress on these questions, and in particular give a complete answer to the second one.
Item Metadata
| Title |
Coloring graphs with forbidden induced subgraphs
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2017-08-24T09:02
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| Description |
The problem of testing if a graph can be colored with a given number $k$ of
colors is NP-complete for every $k>2$. But what if we have more information
about the input graph, namely that some fixed graph $H$ is not present in it
as an induced subgraph? It is known that the problem remains NP-complete
even for $k=3$, unless $H$ is the disjoint union of paths. We consider the
following two questions:
1. For which graphs $H$ is there a polynomial time algorithm to 3-color
(or in general $k$-color) an $H$-free graph?
2. For which graphs $H$ are there finitely many 4-critical $H$-free graphs?
This talk will survey recent progress on these questions, and in particular
give a complete answer to the second one.
|
| Extent |
50 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Princeton University
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| Series | |
| Date Available |
2018-04-12
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0365553
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
|
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International