WebWe show that the total domatic number of a random r-regular graph is almost surely at most r 1, and that for 3-regular random graphs, the total domatic number is almost surely … Web× Close. The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data.

On the total domatic number of regular graphs – DOAJ

WebAn (h,k)-dominating set in a digraph G is a subset D of V(G) such that the subdigraph induced by D is h-connected and for every vertex v of G, v is in-dominated and out-dominated by at least k vertices in D. The (h,k)-domination number @c"h","k(G) of G ... WebWe show that the‎ ‎total domatic number of a random r -regular graph is almost‎ ‎surely at most r − 1 ‎, ‎and that for 3-regular random graphs‎, ‎the‎ ‎total domatic number is almost … phillip island camps

On the fractional total domatic numbers of incidence graphs

Web20 de fev. de 2024 · The fractional domatic number G is defined as F T D ( G) = sup M M r M. In 2024, Goddard and Henning showed that the incidence graph of every complete k -uniform hypergraph H with order n has F T D ( I ( H)) = n n − k + 1 when n ≥ 2 k ≥ 4. We extend the result to the range n > k ≥ 2. WebG is the signed (k,k)-domatic number of G, denoted by dk S(G). First we study basic properties of dk S(G). Some of them are extensions of well-known results on the signed domatic number dS(G) = d1 S(G) given in [6]. Using these results, we determine the signed (k,k)-domatic numbers of fans, wheels and grids. 2. Basic properties of the signed (k ... WebRegular total domatically full graphs are also called rainbow graphs (see, [27, 29]). We first make some easy observations on rainbow graphs. Examples of rainbow graphs … tryout utbk 2022