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
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