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References (17)
-
G. Dirac (1952)
Some Theorems on Abstract GraphsProceedings of The London Mathematical Society
-
P. Erdös (1962)
Remarks on a Paper of PósaMagyar Tud. Akad. Mat. Kutató Int. Közl., 7
-
B. Rothschild (1965)
The Decomposition of Graphs into a Finite Number of PathsCanadian Journal of Mathematics, 17
-
Von Erdos, T. Grunwald, E. Vazsonyi (1938)
ÜBER Euler-Linien Unendlicher GraphenJournal of Mathematics and Physics, 17
-
O. Ore (1967)
The Four-Color Problem -
Frank Zeeuw (2016)
Graph Theory -
C. Nash-Williams (1963)
Decomposition of Graphs into Two-Way Infinite PathsCanadian Journal of Mathematics, 15
-
J. A. Bondy (1969)
Properties of Graphs with Constraints on DegreesStudia Sci. Math. Hungar., 4
-
W. Tutte (1956)
A THEOREM ON PLANAR GRAPHSTransactions of the American Mathematical Society, 82
-
C. St. J. A. Nash-Williams (1968)
Theory of Graphs, Proceedings of the Symposium at Tihany (Hungary), September 1966 -
V. Chvátal (1972)
On Hamilton's idealsJournal of Combinatorial Theory, Series B, 12
-
O. Ore (1962)
Theory of Graphs -
M. Sekanina (1963)
On an Ordering of the Set of Vertices of a GraphČasopis Pěst. Mat., 88
-
C. Nash-Williams (1967)
Infinite graphs—A surveyJournal of Combinatorial Theory, Series A, 3
-
C. Nash-Williams (1966)
Euler Lines in Infinite Directed GraphsCanadian Journal of Mathematics, 18
-
C. Nash-Williams (1966)
On Hamiltonian circuits in finite graphs, 17
-
L. Pósa (1962)
A Theorem Concerning Hamilton LinesMagyar Tud. Akad. Mat. Kutató Int. Közl., 7
- Publisher
- Springer Journals
- Copyright
- Copyright © 1971 by Birkhäuser Verlag
- Subject
- Mathematics; Analysis; Combinatorics
- ISSN
- 0001-9054
- eISSN
- 1420-8903
- DOI
- 10.1007/BF01818692
- Publisher site
- See Article on Publisher Site
Abstract
Hamiltonian Lines in Infinite Graphs with Few Vertices of Small Valency C. ST. J. A. NASH-WILLIAMS (Waterloo, Ontario, Canada) 1. Introduction In this paper, 'iff' will mean 'if and only if'. A set will be called denumerable if its cardinal number is No, and countable if it is finite or denumerable. The set of positive integers will be denoted by P. The set-theoretic notation {al, a2 .... } will mean {ai:ieP}. A right-infinite sequence is an infinite sequence of the form al, a2, a3 .... and a left-infinite sequence is an infinite sequence of the form .... a_3, a_2, a_ 1. Right-infinite and left-infinite sequences will both be called one-way infinite. A two-way infinite sequence is an infinite sequence of the form .... a-2, a-a, ao, al, a2 ..... All graphs considered in this paper are understood to be without loops or multiple edges. The letter G will always denote a graph. The set of vertices of G will be called the vertex-set of G and denoted by V(G), and the set of edges of G will be called the edge-set of G and denoted by E(G). The valency (or degree) of a vertex ~ will be denoted by
Journal
aequationes mathematicae – Springer Journals
Published: May 18, 2005