The signed edge domination number and the signed total edge domination number of a graph are considered; they are variants of the domination number and the total domination number. Some upper bounds for them are found in the case of the $n$-dimensional cube $Q_n$.
Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph G, a hereditary graph property P and l\geqslant 1 we define X{'_{P,l}} to be the minimum number of colours needed to properly colour the edges of G, such that any subgraph of G induced by edges coloured by (at most) l colours is in P. We present a necessary and sufficient condition for the existence of X{'_{P,l}} . We focus on edge-colourings of graphs with respect to the hereditary properties Ok and Sk, where Ok contains all graphs whose components have order at most k+1, and Sk contains all graphs of maximum degree at most k. We determine the value of X{'_{{S_k},l}}(G) for any graph G,k \geqslant 1, l\geqslant 1 and we present a number of results on X{'_{{O_k},l}}(G) ., Samantha Dorfling, Tomáš Vetrík., and Obsahuje seznam literatury
Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi $ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi (u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the domination number of $\pi G$ is equal to the domination number of $G$ for all $\pi $ of $V(G)$. In 1999 it was conjectured that the only universal fixers are the edgeless graphs. Since then, a few partial results have been shown. In this paper, we prove the conjecture completely.
Od počátku roku 2012 je na FF UK v Praze v rámci pětiletého projektu GA ČR připravována kritická čtenářská edice korespondence Karla Havlíčka. Projekt je koncipován jako interdisciplinární (historický a jazykovědný) a navazuje na edici a výzkum korespondence Boženy Němcové. Půjde o první úplnou edici Havlíčkovy korespondence (odeslané i přijaté). Všechny dopisy jsou digitálně fotografovány, transliterovány (transliterační zásady jsou zde otištěny jako příloha) a bude z nich vytvořen počítačový korpus, který mj. napomůže i přesnosti edičního zpracování., Since January 2012, a critical popular edition of Karel Havlíček’s correspondence is being prepared for publication at the Faculty of Arts, Charles University in Prague, with support of Czech Science Foundation. This five-year project is designed as interdisciplinary (historical as well as linguistic) and it builds on the publication and research of the correspondence of Božena Němcová. It is going to be the first complete edition of the letters both written by and addressed to Havlíček. All letters are being shot digitally and transliterated (the manual for transliteration is published here as an appendix); then, a computer language corpus of Karel Havlíček’s correspondence will be built, which-among others-will help in achieving accuracy of the editorial processing. (Translated by Robert Adam.), and Překlad resumé: Robert Adam