Subgraph densities in signed graphons and the local Simonovits-Sidorenko conjecture.
Subsemi-Eulerian graphs.
Sufficient conditions for locally connected graphs
Sufficient conditions on the existence of factors in graphs involving minimum degree
For a set of graphs, an -factor of a graph is a spanning subgraph of , where each component of is contained in . It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the -spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the -spectral radius and the distance...
Sum of squares of degrees in a graph.
Superstable graphs
Sur certaines équations fonctionnelles arithmétiques
Soit le -ième nombre premier. Une fonction arithmétique complètement additive est définie sur par la donnée des et la formule , où désigne la...
Sur le nombre des cycles négatifs d'un graphe complet signé
Sur le problème du couplage maximal
Sur les performances d'algorithmes de recherche de chemins minimaux dans les graphes clairsemés
Survey of spectra of Laplacians on finite symmetric spaces.
The basis number of some special non-planar graphs
The basis number of a graph was defined by Schmeichel to be the least integer such that has an -fold basis for its cycle space. He proved that for , the basis number of the complete bipartite graph is equal to 4 except for , and with . We determine the basis number of some particular non-planar graphs such as and , , and -cages for , and the Robertson graph.
The bichromaticity of a graph
The bigraph decomposition number of a graph
The Borodin-Kostochka conjecture for graphs containing a doubly critical edge.
The cobondage number of a graph
A set D of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V-D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number of G to be the minimum cardinality among the sets of edges X ⊆ P₂(V) - E, where P₂(V) = X ⊆ V:|X| = 2 such that γ(G+X) < γ(G). In this paper, the exact values of bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum type...
The Complexity of Cutting Complexes.
The cost chromatic number and hypergraph parameters
In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
The cover pebbling theorem.
The cover-index of infinite graphs.