The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The projective plane crossing number of the circulant graph C(3k;{1,k})
In this paper we prove that the projective plane crossing number of the circulant graph C(3k;{1,k}) is k-1 for k ≥ 4, and is 1 for k = 3.
The -matrix completion problem.
The quantifier semigroup for bipartite graphs.
The Quest for A Characterization of Hom-Properties of Finite Character
A graph property is a set of (countable) graphs. A homomorphism from a graph G to a graph H is an edge-preserving map from the vertex set of G into the vertex set of H; if such a map exists, we write G → H. Given any graph H, the hom-property →H is the set of H-colourable graphs, i.e., the set of all graphs G satisfying G → H. A graph property P is of finite character if, whenever we have that F ∈ P for every finite induced subgraph F of a graph G, then we have that G ∈ P too. We explore some of...
The Ramsey number.
The ramsey number for theta graph versus a clique of order three and four
For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph on at least N vertices contains F1 or its complement contains F2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(θn,Km) for m = 2, 3, 4 and n > m. More specifically, we establish that r(θn,Km) = (n − 1)(m − 1) + 1 for m = 3, 4 and n > m
The Ramsey number of diamond-matchings and loose cycles in hypergraphs.
The Ramsey number r(C₇,C₇,C₇)
Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.
The Ramsey numbers of large cycles versus small wheels.
The Randić energy of generalized double sun
We show that the family of trees defined as generalized double sun of odd order satisfies the conjecture for the Randić energy proposed by I. Gutman, B. Furtula, S. B. Bozkurt (2014).
The rank of a cograph.
The real symmetric matrices of odd order with a P-set of maximum size
Suppose that is a real symmetric matrix of order . Denote by the nullity of . For a nonempty subset of , let be the principal submatrix of obtained from by deleting the rows and columns indexed by . When , we call a P-set of . It is known that every P-set of contains at most elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step...
The realization of input-output maps using bialgebras.
The Reconstruction of a Connected Graph from its Spanning Trees
The rectilinear crossing number of is 62.
The reflexible hypermaps of characteristic
The Regulation Number of a Graph
The relation between the number of leaves of a tree and its diameter
Let denote the minimum possible number of leaves in a tree of order and diameter Lesniak (1975) gave the lower bound for When is even, But when is odd, is smaller than in general. For example, while In this note, we determine using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.
The remarkable generalized Petersen graph