On some Interconnections Between Combinatorial Optimization and Extremal Graph Theory
On some non-obvious connections between graphs and unary partial algebras
In the present paper we generalize a few algebraic concepts to graphs. Applying this graph language we solve some problems on subalgebra lattices of unary partial algebras. In this paper three such problems are solved, other will be solved in papers [Pió I], [Pió II], [Pió III], [Pió IV]. More precisely, in the present paper first another proof of the following algebraic result from [Bar1] is given: for two unary partial algebras and , their weak subalgebra lattices are isomorphic if and only...
On some partitions of a graph, I
On some problem related to fundamental cycle sets of a graph: Research notes
On some problems in combinatorial set theory.
On some properties of the Laplacian matrix revealed by the RCM algorithm
In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a well-known scheme for numbering the nodes of a network in such a way that the corresponding adjacency matrix has a narrow bandwidth. Inspired by some properties of the eigenvectors of a Laplacian matrix, we derive some properties based on row sums of a...
On some Ramsey and Turán-type numbers for paths and cycles.
On some regularities of graphs. I.
On some regularities of graphs. II.
On some systems of equations with constraints in a free group. – Addenda. (Sur certains systèmes d'équations avec constraintes dans un groupe libre. – Addenda.)
On some systems of equations with constraints in a free group. (Sur certains systèmes d'équations avec contraintes dans un groupe libre.)
On some variations of extremal graph problems
A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) whenever it belongs to P and none of its proper supergraphs of the same order has the property P. A graph is P-extremal if it has a the maximum number of edges among all P-maximal graphs of given order. The number of its edges is denoted by ex(n, P). If the number of edges of a P-maximal...
On Sparse Spanners of Weighted Graphs.
On special structure of graphs having the maximal eigenvalue greater than two.
On spectra of expansion graphs and matrix polynomials. II.
On Spectra of Infinite Graphs
On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs
Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex in the i-th copy of H. The neighborhood corona G★H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. The edge corona G ◇ H is the graph obtained...
On Spectral Structure Of Graphs Having The Maximal Eigenvalue Not Grater Than Two
On Spectrum and Per-spectrum of Graphs
On splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let ℋ be a family of subsets of X which covers each x ∈ X at least κ-fold. What assumptions can ensure that ℋ can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover ℋ: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and covers of ℝⁿ by polyhedra and by arbitrary convex sets. We focus on...