The distinguishing index D′(G) of a graph G is the least number of colours needed in an
edge colouring which is not preserved by any non-trivial automorphism. Broere and Pilśniak …

We consider infinite graphs. The distinguishing number $ D (G) $ of a graph $ G $ is the
minimum number of colours in a vertex colouring of $ G $ that is preserved only by the trivial …

Call a colouring of a graph distinguishing if the only colour preserving automorphism is the
identity. A conjecture of Tucker states that if every automorphism of a connected graph GG …

Dans cette thèse nous étudions trois jeux à objectif compétitif sur les graphes. Les jeux à
objectif compétitif proposent une approche dynamique des problèmes d'optimisation …

The distinguishing number or asymmetric coloring number of a group G on the set Ω,
denoted D (G, Ω) or ACN (G, Ω) is the smallest k such that there is a coloring of Ω by k colors …

Tematem niniejszej rozprawy są kolorowania wierzchołków lub krawędzi grafów, które nie
są zachowywane przez żaden automorfizm danego grafu poza identycznością. Kolorowanie …

Let $ X $ be a connected, locally finite graph with symmetric growth. We prove that there is a
vertex coloring $\phi\colon X\to\{0, 1\} $ and some $ R\in\mathbb {N} $ such that every …