Known borane polyhedral cluster characteristics can be used for predicting new architectural constructs. We propose additional structures derived from B18H22 : three positional isomers different from the well-known anti-B18H22 ...

In the paper ”On the limiting distribution of the metric dimension for random forests” the metric dimension ß(G) of sparse G(n, p) with p = c/n and c < 1 was studied (Theorem 1.2). In the proof of this theorem, for the ...

We present a unified framework to asymptotically count the number of sets, with a given cardinality, free of certain configurations. This is done by combining the hypergraph containers methodology joint with arithmetic ...

Let L be subset of {3,4,…} and let Xn,M(L) be the number of cycles belonging to unicyclic components whose length is in L in the random graph G(n,M). We find the limiting distribution of Xn,M(L) in the subcritical regime ...

Es más que habitual que cuestiones elementales no tengan una respuesta sencilla. Esto ocurre con el enigma con el que iniciaremos esta aventura hacia la combinatoria de los mapas. Deseamos pintar los distintos términos ...

Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with ...

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard ...

It is well-known that the triangulations of the disc with n + 2 vertices on its boundary are counted by the nth Catalan number C(n) = 1 n+1 (2n n ) . This paper deals with the generalisation of this problem to any compact ...

In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ...

This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled ...