𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Extremal maximal uniquely hamiltonian graphs

✍ Scribed by Curtiss A. Barefoot; R. C. Entringer


Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
352 KB
Volume
4
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

Let G be a graph of order n with exactly one Hamiltonian cycle and suppose that G is maximal with respect to this property. We determine the minimum number of edges G can have.


πŸ“œ SIMILAR VOLUMES


A census of maximum uniquely hamiltonian
✍ Curtiss A. Barefoot; R. C. Entringer πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 261 KB πŸ‘ 1 views

## Abstract We show that there are 2^[n/2]‐4^ largest graphs of order __n__ β‰₯ 7 having exactly one hamiltonian cycle. a recursive procedure for constructing these graphs is described.

Vertices of Small Degree in Uniquely Ham
✍ J.A. Bondy; Bill Jackson πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 206 KB

Let G be a uniquely hamiltonian graph on n vertices. We show that G has a vertex of degree at most c log 2 8n+3, where c=(2&log 2 3) &1 r2.41. We show further that G has at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.

Graphs with unique maximal clumpings
✍ Andreas Blass πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 322 KB

## Abstract A partition of the vertices of a graph is called a clumping if, for vertices in distinct partition classes, adjacency depends only on the partition classes, not on the specific vertices. We give a simple necessary and sufficient condition for a finite graph to have a unique maximal clum

Uniqueness of maximal dominating cycles
✍ Herbert Fleischner πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 461 KB πŸ‘ 2 views

## Abstract We construct 3‐regular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ βŠ† __V__(__C__~1~). By a similar construction we obtain loopless 4‐regular graphs having precisely one hamiltonian cycle. The basis for these const

Cubic graphs with three Hamiltonian cycl
✍ Andrew Thomason πŸ“‚ Article πŸ“… 1982 πŸ› John Wiley and Sons 🌐 English βš– 138 KB πŸ‘ 1 views

## Abstract The generalized Petersen graph __P__(6__k__ + 3, 2) has exactly 3 Hamiltonian cycles for __k__ β‰₯ 0, but for __k__ β‰₯ 2 is not uniquely edge colorable. This disproves a conjecture of Greenwell and Kronk [1].

Hamiltonian weights and unique 3-edge-co
✍ Cun-Quan Zhang πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 402 KB

## Abstract A (1,2)‐eulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3‐connected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3‐