Publication:
Internally 4-Connected Graphs with No {Cube, V<inf>8</inf>}-Minor

dc.contributor.authorChanun Lewchalermvongsen_US
dc.contributor.authorNawarat Ananchuenen_US
dc.contributor.otherMahidol Universityen_US
dc.date.accessioned2022-08-04T08:56:44Z
dc.date.available2022-08-04T08:56:44Z
dc.date.issued2021-05-01en_US
dc.description.abstractA 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.en_US
dc.identifier.citationDiscussiones Mathematicae - Graph Theory. Vol.41, No.2 (2021), 481-501en_US
dc.identifier.doi10.7151/dmgt.2205en_US
dc.identifier.issn20835892en_US
dc.identifier.issn12343099en_US
dc.identifier.other2-s2.0-85100555636en_US
dc.identifier.urihttps://repository.li.mahidol.ac.th/handle/20.500.14594/77381
dc.rightsMahidol Universityen_US
dc.rights.holderSCOPUSen_US
dc.source.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85100555636&origin=inwarden_US
dc.subjectMathematicsen_US
dc.titleInternally 4-Connected Graphs with No {Cube, V<inf>8</inf>}-Minoren_US
dc.typeArticleen_US
dspace.entity.typePublication
mu.datasource.scopushttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85100555636&origin=inwarden_US

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