Note on the factors of graphs.
Note On The Game Colouring Number Of Powers Of Graphs
We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.
Note on the gammoids arising from undirected graphs
Note on the number of monoids of order
Note on the regular digraphs
Note on the relation between radius and diameter of a graph
The known relation between the standard radius and diameter holds for graphs, but not for digraphs. We show that no upper estimation is possible for digraphs. We also give some remarks on distances, which are either metric or non-metric.
Note on the split domination number of the Cartesian product of paths
In this note the split domination number of the Cartesian product of two paths is considered. Our results are related to [2] where the domination number of Pₘ ☐ Pₙ was studied. The split domination number of P₂ ☐ Pₙ is calculated, and we give good estimates for the split domination number of Pₘ ☐ Pₙ expressed in terms of its domination number.
Note on the weight of paths in plane triangulations of minimum degree 4 and 5
The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P₅ on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P₄ on 4 vertices of weight at most 31.
Note on transformations of posets with the same upper bound graph and minimal elements.
Note on Turán's graph
Note on weak epimorphisms of -nets without singular points
Note: random-to-front shuffles on trees.
Note relative aux intersections intérieures des diagonales d'un polygone convexe
Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs
Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 □G2 of G1 and G2. We show that: [...] and [...] . We also characterize the graphs for which equality holds. As a by-product we derive a formula for the number of spanning trees in Kn1 □Kn2 which turns out to be [...] .
Note sur la marche du cavalier dans un échiquier
Note sur la partition des nombres
Note sur le nombre des marches rentrantes, que l'on peut obtenir en remplissant successivement les deux demi-échiquiers rectangulaires ayant pour frontière commune l'une des médianes de l'échiquier total
Note sur le théorème des demi-degrés
Note sur les coefficients du binôme de Newton
Note sur les permutations de objets et sur leur classement