Browsing by Author "Schiermeyer, Ingo"

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Access status: Restricted ,
Frequency assignment in mobile networks - analysis of algorithms
(Data obrony: 2014-07-07) Lalewicz, Anna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Frequency assignment in mobile networks and its practical implementation
(Data obrony: 2014-07-07) Więcek, Witold
Wydział Matematyki Stosowanej
Access status: Restricted ,
Frequency assignment in mobile networks in terms of linear programming
(Data obrony: 2014-07-07) Wójcik, Piotr
Wydział Matematyki Stosowanej
Access status: Restricted ,
Maximum independent set problem in graphs
(Data obrony: 2014-07-07) Wideł, Wojciech
Wydział Matematyki Stosowanej
Access status: Open Access ,
On the chromatic number of (P5,windmill)-free graphs
(Wydawnictwa AGH, 2017) Schiermeyer, Ingo
In this paper we study the chromatic number of $(P_{5},windmill)$-free graphs. For integers $r,p\geq 2$ the windmill graph $W_{r+1}^p=K_1 \vee pK_r$ is the graph obtained by joining a single vertex (the center) to the vertices of $p$ disjoint copies of a complete graph $K_r$. Our main result is that every $(P_{5},windmill)$-free graph $G$ admits a polynomial $\chi$-binding function. Moreover, we will present polynomial $\chi$-binding functions for several other subclasses of $P_{5}$-free graphs.
Access status: Open Access ,
[r, s, t]-colourings of paths
(2007) Salvador Villá, Marta; Schiermeyer, Ingo
The concept of $[r,s,t]$-colourings was recently introduced by Hackmann, Kemnitz and Marangio [A. Kemnitz, M. Marangio, $[r,s,t]$-Colorings of Graphs, Discrete Math., to appear] as follows: Given non-negative integers $r$, $s$ and $t$, an $[r,s,t]$-colouring of a graph $G=(V(G),E(G))$ is a mapping $c$ from $V(G) \cup E(G)$ to the colour set $\{1,2,\ldots ,k\}$ such that $|c(v_i)-c(v_j)| \geq r$ for every two adjacent vertices $v_{i}$, $v_{j}$, $|c(e_i)-c(e_j)| \geq s$ for every two adjacent edges $e_{i}$, $e_{j}$, and $|c(v_i)-c(e_j)| \geq t$ for all pairs of incident vertices and edges, respectively. The $[r,s,t]$-chromatic number $\chi_{r,s,t}(G)$ of $G$ is defined to be the minimum $k$ such that $G$ admits an $[r,s,t]$-colouring. In this paper, we determine the $[r,s,t]$-chromatic number for paths.
Access status: Restricted ,
Rainbow connection in graphs
(Data obrony: 2014-07-07) Karp, Damian
Wydział Matematyki Stosowanej