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Cerf Theory for Graphs

Journal of the London Mathematical Society, 1998
This paper develops a deformation theory for \(k\)-parameter families of pointed marked graphs with fixed fundamental group \(F_n\). Applications include a simple geometric proof of stability of the rational homology of \(\Aut(F_n)\), computations of the rational homology of \(\Aut(F_n)\) in small dimensions, proofs that various natural complexes of ...
Hatcher, Allen, Vogtmann, Karen
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On a Problem in Graph Theory

The Mathematical Gazette, 1963
Suppose there are n towns every pair of which are connected by a single one-way road (roads meet only at towns). Is it possible to choose the direction of the traffic on all the roads so that if any two towns are named there is always a third from which the two named can be reached directly ...
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Chemical Graph Theory

2013
This chapter on chemical graph theory forms part of the natural science and processes section of the ...
Estrada, Ernesto, Bonchev, Danail
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Graph Theory and Probability

Canadian Journal of Mathematics, 1959
A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent
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Cabri-graph, a sketchpad for graph theory

Mathematics and Computers in Simulation, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baudon, Olivier, Laborde, Jean-Marie
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A ring in graph theory

Mathematical Proceedings of the Cambridge Philosophical Society, 1947
We call a point set in a complex K a 0-cell if it contains just one point of K, and a 1-cell if it is an open arc. A set L of 0-cells and 1-cells of K is called a linear graph on K if(i) no two members of L intersect,(ii) the union of all the members of L is K,(iii) each end-point of a 1-cell of L is a 0-cell of Land (iv) the number of 0-cells and 1 ...
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Graph Theory and Definitions

2019
Graphs are a mathematical structure composed of a set of elements, and a set of connection between them. Due to their intuitive representation, graphs are widely employed in many different fields and, in particular, in systems biology and bioinformatics.
Beretta S., Denti L., Previtali M.
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Introduction to Graph Theory

1995
The objects that we study in the branch of mathematics known as graph theory are not graphs drawn with x and y axes. In this chapter, the word ‘graph’ refers to a structure consisting of points (called ‘vertices’), some of which may be joined to other vertices by lines (called ‘edges’) to form a network. Structures of this type abound in computing. The
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Reflections on graph theory

Journal of Graph Theory, 1986
AbstractAt the occasion of the 250th anniversary of graph theory, we recall some of the basic results and unsolved problems, some of the attractive and surprising methods and results, and some possible future directions in graph theory.
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A theory of degeneracy graphs

Annals of Operations Research, 1993
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