A note on immersion minors and planarity |
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Authors: | Donald K Wagner |
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Institution: | Mathematical, Computer, and Information Sciences Division, Office of Naval Research, Arlington, VA 22203, USA |
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Abstract: | Graph minors play an important role in graph theory. The focus of this paper is on immersion minors and their relationship to planarity. In general, planar graphs can have non-planar immersion minors. This paper shows that by placing a simple restriction on the immersion-minor operations, all immersion minors of a planar graph are planar. This then allows one to easily obtain a characterization of planar graphs using immersion minors. A dual form of this characterization, as well as an extension to binary matroids, are also considered. |
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Keywords: | Graph immersion Graph minors |
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