HAMILTONIAN CIRCLES AND PATHS IN DIRECTED GRAPHS

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10 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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HAMILTONIAN CIRCLES AND PATHS IN DIRECTED GRAPHS


Author:

SZÜGYI Judit

Mentor:

dr.
Vojislav PETROVIĆ,
full professor

Institution:

University of Novi Sad, Faculty of Natural Sciences, Department of
Mathematics and Informatics, Pedagogue of Mathematics

Hungar
ian College for Higher Education in Vojvodina


In the introduction, I introduce some basic terms related to graphs, directed
graphs. In the main part of my work I analyse the theorems about Hamiltonian circles
and paths of directed graphs. I prove Meyniel
’s theorem, which gives sufficient condition
for a non
-
trivial strongly connected digraph to include a Hamiltonian circle. With the
help this theorem I prove the Ghouil
-
Houri’s and Woodall’s theorem, which also give
sufficient condition for strongly connec
ted and for any graphs to include a Hamiltonian
circle. I prove that Overbeck
-
Larisch’s theorem gives sufficient condition for any two
vertices of a digraph to be connected by a Hamiltonian path. The consequences of these
theorems give some other sufficien
t conditions for a digraph to include a Hamiltonian
circe. The aim of my work is to introduce and prove the theorems above with their
consequences and to compare the strength of the conditions of these theorems.


Key words:

directed graph, Hamiltonian circles, Hamiltonian path, sufficient conditions