Publication: Internally 4-Connected Graphs with No {Cube, V<inf>8</inf>}-Minor
Issued Date
2021-05-01
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20835892
12343099
12343099
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2-s2.0-85100555636
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Mahidol University
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SCOPUS
Bibliographic Citation
Discussiones Mathematicae - Graph Theory. Vol.41, No.2 (2021), 481-501
Suggested Citation
Chanun Lewchalermvongs, Nawarat Ananchuen Internally 4-Connected Graphs with No {Cube, V<inf>8</inf>}-Minor. Discussiones Mathematicae - Graph Theory. Vol.41, No.2 (2021), 481-501. doi:10.7151/dmgt.2205 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/77381
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Internally 4-Connected Graphs with No {Cube, V<inf>8</inf>}-Minor
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Abstract
A simple graph is a minor of another if the first is obtained from the second by deleting vertices, deleting edges, contracting edges, and deleting loops and parallel edges that are created when we contract edges. A cube is an internally 4-connected planar graph with eight vertices and twelve edges corresponding to the skeleton of the cube in the platonic solid, and the Wagner graph V8 is an internally 4-connected nonplanar graph obtained from a cube by introducing a twist. A complete characterization of all internally 4-connected graphs with no V8 minor is given in J. Maharry and N. Robertson, The structure of graphs not topologically containing the Wagner graph, J. Combin. Theory Ser. B 121 (2016) 398-420; on the other hand, only a characterization of 3-connected graphs with no cube minor is given in J. Maharry, A characterization of graphs with no cube minor, J. Combin. Theory Ser. B 80 (2008) 179-201. In this paper we determine all internally 4-connected graphs that contain neither cube nor V8 as minors. This result provides a step closer to a complete characterization of all internally 4-connected graphs with no cube minor.