Results 71 to 80 of about 280 (99)

On Eulerian and Hamiltonian Graphs and Line Graphs

Canadian Mathematical Bulletin, 1965
A graph G has a finite set V of points and a set X of lines each of which joins two distinct points (called its end-points), and no two lines join the same pair of points. A graph with one point and no line is trivial. A line is incident with each of its end-points. Two points are adjacent if they are joined by a line.
Harary, Frank, Nash-Williams, C. S. J. A.   +1 more
exaly   +3 more sources

Eulerian Subgraphs in 3-Edge-Connected Graphs and Hamiltonian Line Graphs

Journal of Graph Theory, 2003
Abstract In this paper, we show that if G is a 3‐edge‐connected graph with $S \subseteq V(G)$ and $|S| \le 12$
Hong-Jian Lai, Xiangwen Li, Deying Li
exaly   +4 more sources

Traversing Graphs: The Eulerian and Hamiltonian Theme

2000
This chapter deals with basic graph theoretical concepts and then focuses on special topics which are — in their applications — of relevance to theoretical and practical problems in OR. Therefore, this chapter is structured as follows: 1. Basics of Graph Theory. 2. Connectivity, Menger’s Theorem, the Splitting Lemma, and Factors.
Herbert Fleischner
exaly   +2 more sources

Graph Theoretical Logic of Organic Chemistry Nomenclature: Why Eulerian Paths Are Better Suited for Aliphatic Compounds Versus Hamiltonian Paths for Benzenoids

Computational and Theoretical Chemistry, 1999
Abstract The model selected in order to assign a canonical name to a molecule in organic chemistry usually uses a graph theoretical edge set joining carbon nodes. For aliphatic compounds the most efficient type nomenclature involves the concatenation of Eulerian paths.
exaly   +2 more sources

Hamiltonian and Eulerian Properties of Entire Graphs

Lecture Notes in Mathematics, 1972
John Mitchem
exaly   +2 more sources

Eulerian Multigraphs and Hamiltonian Graphs

2007
exaly   +5 more sources

Collapsible Graphs and Hamiltonian Connectedness of Line Graphs

Discrete Applied Mathematics, 2012
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Chen and Lai [Z.-H. Chen, H.-J. Lai, Reduction techniques for super-Eulerian graphs and related topics an update, in: Ku Tung-Hsin (Ed.), Combinatorics and Graph Theory, vol.
Weihua Yang
exaly   +2 more sources

A Novel Characterization of Cubic Hamiltonian Graphs via the Associated Quartic Graphs [PDF]

Ars Mathematica Contemporanea, 2017
We give a necessary and sufficient condition for a cubic graph to be Hamiltonian by analyzing Eulerian tours in certain spanning subgraphs of the quartic graph associated with the cubic graph by 1-factor contraction. This correspondence is most useful in
Tomaž Pisanski
exaly   +2 more sources

On Eulerian subgraphs and hamiltonian line graphs [PDF]

, 2023
A graph {\color{black}$G$} is Hamilton-connected if for any pair of distinct vertices {\color{black}$u, v \in V(G)$}, {\color{black}$G$} has a spanning $(u,v)$-path; {\color{black}$G$} is 1-hamiltonian if for any vertex subset $S \subseteq {\color{black ...
xie, yikang
openaire   +2 more sources

Eulerian and Hamiltonian Graphs

2000
The study of Eulerian graphs was initiated in the 18th century and that of Hamiltonian graphs in the 19th century. These graphs possess rich structures; hence, their study is a very fertile field of research for graph theorists. In this chapter, we present several structure theorems for these graphs.
Joan M. Aldous, Robin J. Wilson
openaire   +2 more sources