We consider a two-variable guarded fragment with number restrictions for binary relations and give a satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment. The translation can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. This allows...

The average size of connected vertex subsets a graph generalises much-studied parameter for subtrees trees. For trees, the possible values this are critically affected by presence or absence vertices degree 2. We answer two questions Andrew Vince regarding effect constraints on general graphs. give new lower bound, and first non-trivial upper maximum growth rate number sets cubic graph, in fact...

The topic is the average order A(G) of a connected induced subgraph graph G. This generalizes, to graphs in general, subtree tree. In 1983 Jamison proved that order, over all trees n, minimized by path Pn, being A(Pn)=(n+2)/3. 2018, Kroeker, Mol, and Oellermann conjectured Pn minimizes G - conjecture was recently proved. this short note we show lower bound can be improved if connectivity known....