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Anti-Ramsey numbers for disjoint copies of graphs

Gorgol I., Gorlich A.

Opuscula Mathematica

2017

Vol. 37, no. 4

567--575

A subgraph of an edge-colored graph is called rainbow if all of its edges have different colors. For a graph G and a positive integer n, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of H. Anti-Ramsey numbers were introduced by Erdos, Simonovits and Sós and studied in numerous papers. Let G be a graph with anti-Ramsey number ar(n, G). In this paper we show the lower bound for ar(n,pG), where pG denotes p vertex-disjoint copies of G. Moreover, we prove that in some special cases this bound is sharp.

Wolfram demonstrations project platform as a support in teaching

Gorgol I

Advances in Science and Technology. Research Journal

2015

Vol. 9, nr 26

143--147

The article presents how Wolfram Demonstrations Project platform can support teaching of a great variety of subjects from very basic up to university level. The Wolfram Demonstrations Project is part of the family of free online services from Wolfram Research. General overview of the platform will be presented as well as a particular usage. The application concerns presenting to students certain numerical methods, namely one-step methods for Cauchy problem for ordinary differential equations.