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● H e l p ● L e a r n t o e d i t ● C o m m u n i t y p o r t a l ● R e c e n t c h a n g e s ● U p l o a d f i l e
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( T o p )
1 H i s t o r y
2 R e f e r e n c e s
3 E x t e r n a l l i n k s
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A p p e a r a n c e
F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
History [ edit ]
Hypohamiltonian graphs were first studied by Sousselier in Problèmes plaisants et délectables (1963).[1] [2] [3] [4]
From the start, the smallest hypohamiltonian graph is known: the Petersen graph . However, the hunt for the smallest planar hypohamiltonian graph continues. This question was first raised by Václav Chvátal in 1973.[5] Carsten Thomassen , who exhibited a 105-vertices construction, the 105-Thomassen graph .[6] planar hypohamiltonian graph on 57 vertices : the Hatzel graph .[7] 48-Zamfirescu graph .[8]
In 2009, a graph built by Gábor Wiener and Makoto Araya became (with its 42 vertices) the smallest planar hypohamiltonian graph known.[9] [10] 42 answer to The Ultimate Question of Life, the Universe, and Everything from The Hitchhiker's Guide to the Galaxy , a Douglas Adams novel. However, subsequently, smaller planar hypohamiltonian graphs have been discovered.[11]
References [ edit ]
^ Sousselier, R. (1963), Problème no. 29: Le cercle des irascibles , vol. 7, Rev. Franç. Rech. Opérationnelle, pp. 405–406
^ Lindgren, W. F. (1967), "An infinite class of hypohamiltonian graphs", American Mathematical Monthly 74 9 ): 1087–1089, doi :10.2307/2313617 , JSTOR 2313617 , MR 0224501
^ Gaudin, T.; Herz, P.; Rossi (1964), "Solution du problème No. 29", Rev. Franç. Rech. Opérationnelle (in French), 8
^ Busacker, R. G.; Saaty, T. L. (1965), Finite Graphs and Networks
^ Chvátal, V. (1973), "Flip-flops in hypo-Hamiltonian graphs", Canadian Mathematical Bulletin 16 doi :10.4153/cmb-1973-008-9 MR 0371722
^ Thomassen, Carsten (1976), "Planar and infinite hypohamiltonian and hypotraceable graphs", Discrete Mathematics 14 4 ): 377–389, doi :10.1016/0012-365x(76 )90071-6 , MR 0422086
^ Hatzel, Wolfgang (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Mathematische Annalen 243 (3 ): 213–216, doi :10.1007/BF01424541 , MR 0548801 , S2CID 121794449
^ Zamfirescu, Carol T.; Zamfirescu, Tudor I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory 55 4 ): 338–342, doi :10.1002/jgt.20241 , MR 2336805 , S2CID 260477281
^ Wiener, Gábor; Araya, Makoto (April 20, 2009), The ultimate question , arXiv :0904.3012 Bibcode :2009arXiv0904.3012W
^ Wiener, Gábor; Araya, Makoto (2011), "On planar hypohamiltonian graphs", Journal of Graph Theory 67 1 ): 55–68, doi :10.1002/jgt.20513 , MR 2809563 , S2CID 5340663
^ Jooyandeh, Mohammadreza; McKay, Brendan D. ; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar hypohamiltonian graphs on 40 vertices", Journal of Graph Theory 84 2 ): 121–133, arXiv :1302.2698 doi :10.1002/jgt.22015 , MR 3601121 , S2CID 5535167
External links [ edit ]
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Wiener–Araya_graph&oldid=1188570060 " C a t e g o r i e s : ● I n d i v i d u a l g r a p h s ● P l a n a r g r a p h s H i d d e n c a t e g o r i e s : ● C S 1 F r e n c h - l a n g u a g e s o u r c e s ( fr ) ● C S 1 G e r m a n - l a n g u a g e s o u r c e s ( de )
● T h i s p a g e w a s l a s t e d i t e d o n 6 D e c e m b e r 2 0 2 3 , a t 0 7 : 0 3 ( U T C ) . ● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
