Tuza, An Upper Bound on the Number of Cliques in a Graph, Networks 23 (1993) 207-210.An upper bound on the number of cliques in a graph, Networks - Tuza - 1993M. Farber, M. Hujter, and Z. Tuza, An upper bound on the number of cliques in a graph, Networks 23 (1993), 207...
The maximum number of cliques in graphs without long cyclesRuth Luo ∗September 13, 2017AbstractThe Erd˝ os–Gallai Theorem states that for k ≥ 3 every graph on n vertices with more than12 (k − 1)(n − 1) edges contains a cycle of length at least k. Kopylov proved a ...
The strong chromatic index of G is equal to the chromatic number of the square of the line graph of G. The chromatic number of the square of the line graph of G is greater than or equal to the clique number of the square of the line graph of G, denoted by ω(L). In this note...
On this paper, we fix the number of cliques that cover a graph by the same number of vertices that the graph has, and give an upper bound for the sum of the number of vertices of these cliques in the cases where this covering is possible. 关键词: Mathematics - Combinatorics DOI: ...
We consider the subchromatic number χS(G) of graph G, which is the minimum order of all partitions of V(G) with the property that each class in the partition induces a disjoint union of cliques. Here we establish several bounds on subchromatic number. For example, we consider the maximu...
Clique-transversal sets and weak 2-colorings in graphs of small maximum degree Graph coloring and related topics of cliques, independence numbers, and graph factorization are addressed next. Graph Theory and Its Applications, 2d ed More results ► Encyclopedia browser ? ▲ indelible ink indemnificat...
g = ig.Graph.Famous('Krackhardt_Kite') g.cliques(min=3,max=3) [(0,1,3), (0,2,3), (0,2,5), (0,3,5), (1,3,4), (1,3,6), (1,4,6), (2,3,5), (3,4,6), (3,5,6), (5,6,7)] So the number of triangles should be return like this (based on Gephi) ...
Also, the graph can be further simplified since some edges with weight <=4 can be skipped when searching the cliques. Pruning network and searching afterwards should be more efficient than iterating over all possible combinations. If you are interested in the details, please refer...
We consider the subchromatic number X_S(G) of graph G, which is the minimum order of all partitions of V(G) with the property that each class in the partition induces a disjoint union of cliques. Here we established several bounds on subchromatic number. For example, we consider the ...
In the latter case, we consider the maximum cardinality of a set of vertices that are mutually at maximum distance, that is d=D, where D is the diameter of G. In particular, in Section 4, we study the existence and properties of d-cliques (also called d-spreads in the literature), ...