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Alexopoulos T Allen C Anderson EW Areti H Banerjee S Beery PD Biswas NN Bujak A Carmony DD Carter T Cole P Choi Y De Bonte RJ Erwin AR Findeisen C Goshaw AT Gutay LJ Hirsch AS Hojvat C Kenney VP Lindsey CS LoSecco JM McMahon T McManus AP Morgan N Nelson KS Oh SH Piekarz J Porile NT Reeves D Scharenberg RP Stampke SR Stringfellow BC Thompson MA Turkot F Walker WD Wang CH Wesson DK 《Physical review letters》1990,64(9):991-994
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Aihara H Alston-Garnjost M Avery RE Barbaro-Galtieri A Barker AR Barnes AV Barnett BA Bauer DA Bengtsson H Bintinger DL Bobbink GJ Bolognese TS Bross AD Buchanan CD Buijs A Cain MP Caldwell DO Clark AR Cowan GD Crane DA Dahl OI Derby KA Eastman JJ Eberhard PH Eisner AM Enomoto R Erné FC Fujii T Gary JW Gorn W Hauptman JM Hofmann W Huth JE Hylen J Kamae T Kaye HS Kees KH Kenney RW Kerth LT Ko W Koda RI Kofler RR Kwong KK Lander RL Langeveld WG Layter JG Linde FL Lindsey CS Loken SC Lu A Lu X 《Physical review letters》1986,57(8):945-948
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Lazarus EA Navratil GA Greenfield CM Strait EJ Austin ME Burrell KH Casper TA Baker DR DeBoo JC Doyle EJ Durst R Ferron JR Forest CB Gohil P Groebner RJ Heidbrink WW Hong R Houlberg WA Howald AW Hsieh C Hyatt AW Jackson GL Kim J Lao LL Lasnier CJ Leonard AW Lohr J La Haye RJ Maingi R Miller RL Murakami M Osborne TH Perkins LJ Petty CC Rettig CL Rhodes TL Rice BW Sabbagh SA Schissel DP Scoville JT Snider RT Staebler GM Stallard BW Stambaugh RD St John HE Stockdale RE Taylor PL Thomas DM 《Physical review letters》1996,77(13):2714-2717
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Aihara H Alston-Garnjost M Bakken JA Barbaro-Galtieri A Barnes AV Barnett BA Bengtsson H Blumenfeld BJ Bross AD Buchanan CD Chamberlain O Chien C Clark AR Cordier A Dahl OI Day CT Derby KA Eberhard PH Fancher DL Fujii H Fujii T Gabioud B Gary JW Gorn W Hadley NJ Hauptman JM Hofmann W Huth JE Hylen J Kamae T Kaye HS Kenney RW Kerth LT Koda RI Kofler RR Kwong KK Layter JG Lindsey CS Loken SC Lu X Lynch GR Madansky L Madaras RJ Maruyama K Marx JN Matthews JA Melnikoff SO Moses W Nemethy P 《Physical review letters》1985,54(4):270-273
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A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once.In this paper,we study 1-planar graph joins.We prove that the join G + H is 1-planar if and only if the pair [G,H] is subgraph-majorized by one of pairs [C3 ∪ C3,C3],[C4,C4],[C4,C3],[K2,1,1,P3] in the case when both elements of the graph join have at least three vertices.If one element has at most two vertices,then we give several necessary/sufficient conditions for the bigger element. 相似文献
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I. Fabrici J. Harant T. Madaras S. Mohr R. Soták C. T. Zamfirescu 《Journal of Graph Theory》2020,95(1):125-137
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. 相似文献