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Long cycles and spanning subgraphs of locally maximal 1-planar graphs [Elektronski vir]Fabrici, Igor ...A graph is 1-planar if it has a drawing in the plane such that each edge is crossed at most once by another edge. Moreover, if this drawing has the additional property that for each crossing of two ... edges the end vertices of these edges induce a complete subgraph, then the graph is locally maximal 1-planar. For a 3-connected locally maximal 1-planar graph G, we show the existence of a spanning 3-connected planar subgraph and prove that G is Hamiltonian if G has at most three 3-vertex-cuts, and that G is traceable if G has at most four 3-vertex-cuts. Moreover, infinitely many nontraceable 5-connected 1-planar graphs are presented.Source: Journal of graph theory [Elektronski vir]. - ISSN 1097-0118 (Vol. 95, iss. 1, 2020, str. 125-137)Type of material - e-article ; adult, seriousPublish date - 2020Language - englishCOBISS.SI-ID - 109727235
Author
Fabrici, Igor |
Harant, Jochem |
Madaras, Tomáš |
Mohr, Samuel |
Soták, Roman |
Zamfirescu, Carol T.
Topics
Hamiltonicity |
longest cycle |
1-planar graph |
spanning subgraph
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Fabrici, Igor | |
Harant, Jochem | |
Madaras, Tomáš | |
Mohr, Samuel | |
Soták, Roman | 36239 |
Zamfirescu, Carol T. |
Source: Personal bibliographies
and: SICRIS
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