On hypohamiltonian graphs

✍ Scribed by Carsten Thomassen

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 996 KB
• Volume: 10
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(74)90128-9

✦ Synopsis

Rewived 22 January 1974 ct. Herz, Duby and Vigw! [9] wnjectured that every hyguhamiltonian 3 5. In the present note hypohamil tonian graphs of girth 3 and 4 are dewribed. Alsa two con-jectur~s on hypahtimiItoni;in graphs made by Bone@ and Chva"d, respectkply, are disproved. e adopt the notation and terminology of Harary [$] with tile modifications that the terms verlkes and ec&~ ze here used instead of the terms padnts and lines, respectively, in f 8 1. The set of verti tively edges, of the graph G is deno'ted by k'(G), respective edl;l,e joining the vertices ,I: and y is denoted by (x, y) and ( y, .x) and the!! degree of x in G is e;le:noted by d(x, G j, ph G is hy~utta;-rz~~~~n~~~~ if and only if G is not errtexdeieted subgraph G --u is Hamiltonian. graphs were first studied by Sousseiier (see [ 1 z 21) who a thirrgs proved at the Petersen graph is the smallest and Vigue" [ 9 ] ved that: there exists no hypohamiltonian graph *G&h 11 or 12 vertices. Infinite