Abstract In this work we analyse bucket increasing tree families. We introduce two simple stochastic growth processes, generating random trees of size n , complementing the earlier result Mahmoud and Smythe (1995, Theoret. Comput. Sci. 144 221–249.) for recursive trees. On combinatorial side, define multilabelled generalisations families d -ary generalised plane-oriented Additionally, a cluster...

For a fixed graph $H$, what is the smallest number of colors $C$ such that there proper edge-coloring complete $K_n$ with containing no two vertex-disjoint color-isomor...

Neighborhood Lights Out is a game played on graphs. Begin with graph and vertex labeling of the from set $\{0,1,2,\dots, \ell-1\}$ for $\ell \in \mathbb{N}$. The by toggling vertices: when toggled, that each its neighbors has label increased $1$ (modulo $\ell$). won every 0. For any $n\in\mathbb{N}$ it clear one cannot win $K_n$ unless initial assigns all vertices same label. Given maximum numb...