Browsing by Subject "digraph"

Now showing 1 - 7 of 7

Access status: Restricted ,
Hipoteza Caccetty-Häggkvista
(Data obrony: 2018-10-18) Jamróz, Barbara
Wydział Matematyki Stosowanej
Access status: Restricted ,
O digrafach objazdowo jednorodnych
(Data obrony: 2012-10-29) Mazur, Monika
Wydział Matematyki Stosowanej
Access status: Open Access ,
On arc-coloring of digraphs
(2006) Zwonek, Małgorzata
In the paper we deal with the problem of the arc-colouring of some classes of digraphs (tournaments, complete digraphs and products of digraphs).
Access status: Restricted ,
Regularyzacja grafów
(Data obrony: 2010-10-27) Majmurek, Anna
Wydział Matematyki Stosowanej
Access status: Open Access ,
Toward Wojda's conjecture on digraph packing
(Wydawnictwa AGH, 2017) Konarski, Jerzy; Żak, Andrzej
Given a positive integer $m\leq n/2$, Wojda conjectured in 1985 that if $D_1$ and $D_2$ are digraphs of order n such that $|A(D_1)|\leq n−m$ and $|A(D_2)|\leq 2n-\lfloor n/m\rfloor-1$ then $D_1$ and $D_2$ pack. The cases when $m=1$ or $m=n/2$ follow from known results. Here we prove the conjecture for $m\geq\sqrt{8n}+418275$.
Access status: Restricted ,
Warunek typu Meyniela na hamiltonowskość digrafów dwudzielnych
(Data obrony: 2016-10-28) Kłosowski, Adrian
Wydział Matematyki Stosowanej
Access status: Open Access ,
Weak signed Roman k-domination in digraphs
(Wydawnictwa AGH, 2024) Volkmann, Lutz
Let $k \geq 1$ be an integer, and let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman $k$-dominating function (WSRkDF) on a digraph $D$ is a function $f \colon V(D)\rightarrow \{-1,1,2\}$ satisfying the condition that $\sum_{x \in N^-[v]}f(x)\geq k$ for each $v \in V(D)$, where $N^-[v]$ consists of $v$ and all vertices of $D$ from which arcs go into $v$. The weight of a WSRkDF $f$ is $w(f)=\sum_{v\in V(D)}f(v)$. The weak signed Roman $k$-domination number $\gamma_{wsR}^k(D)$ is the minimum weight of a WSRkDF on $D$. In this paper we initiate the study of the weak signed Roman $k$-domination number of digraphs, and we present different bounds on $\gamma_{wsR}^k(D)$. In addition, we determine the weak signed Roman $k$-domination number of some classes of digraphs. Some of our results are extensions of well-known properties of the weak signed Roman domination number $\gamma_{wsR}(D)=\gamma_{wsR}^1(D)$ and the signed Roman $k$-domination number $\gamma_{sR}^k(D).$