Browsing by Subject "graph theory"

Now showing 1 - 8 of 8

Access status: Open Access ,
A note on possible density and diameter of counterexamples to the Seymour's second neighborhood conjecture
(Wydawnictwa AGH, 2021) Zelenskiy, Oleksiy; Darmosiuk, Valentyna; Nalivayko, Illia
Seymour's second neighborhood conjecture states that every simple digraph without loops or 2-cycles contains a vertex whose second neighborhood is at least as large as its first. In this paper we show, that from falsity of Seymour's second neighborhood conjecture it follows that there exist strongly-connected counterexamples with both low and high density (dense and sparse graph). Moreover, we show that if there is a counterexample to conjecture, then it is possible to construct counterexample with any diameter $k \geq 3$.
Access status: Restricted ,
Dekompozycje i pakowania grafów na podgrafy rozmiaru 3
(Data obrony: 2020-07-15) Górka, Izabela
Wydział Matematyki Stosowanej
Access status: Restricted ,
Gry na grafach
(Data obrony: 2015-06-11) Janik, Bartosz
Wydział Matematyki Stosowanej
Access status: Restricted ,
Kombinatoryka dla programistów
(Wydawnictwa Naukowo-Techniczne, 2007) Lipski, Witold
Access status: Restricted ,
Liczba Turána dla rzadkich grafów rozpinających
(Data obrony: 2016-06-08) Pastuszczak, Marcelina
Wydział Matematyki Stosowanej
Access status: Open Access ,
The forwarding indices of graphs - a survey
(2013) Xu, Jun-Ming; Xu, Min
A routing $R$ of a connected graph $G$ of order n is a collection of $n(n-1)$ simple paths connecting every ordered pair of vertices of $G$. The vertex-forwarding index $\xi(G,R)$ of $G$ with respect to a routing $R$ is defined as the maximum number of paths in $R$ passing through any vertex of $G$. The vertex-forwarding index $\xi(G)$ of $G$ is defined as the minimum $\xi(G,R)$ over all routings $R$ of $G$. Similarly, the edge-forwarding index $\pi(G,R)$ of $G$ with respect to a routing $R$ is the maximum number of paths in $R$ passing through any edge of $G$. The edge-forwarding index $\pi(G)$ of $G$ is the minimum $\pi(G,R)$ over all routings $R$ of $G$. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.
Access status: Restricted ,
Twierdzenie Brooksa dla rozróżniającej liczby chromatycznej
(Data obrony: 2014-09-11) Wojciechowski, Marcin
Wydział Matematyki Stosowanej
Access status: Open Access ,
Using erlang in research and education in a technical university
(Wydawnictwa AGH, 2018) Petrov, Iurii; Alexeyenko, Andrey; Ivanova, Galina
This paper addresses the problem of using functional programming (FP) languages for research and educational purposes. In order to identify the problems associated with the use of FP languages such as Erlang, an experiment consisting of two surveys was performed. The first survey was anonymous and aimed at establishing whether the participants prefer object-oriented or functional coding. The second one was a survey made after the students finished an Erlang course. The results of these two surveys demonstrate that functional programming is underrated with no apparent reasons. Possible steps to address this problem are suggested.