Year 2025

• Mobile mutual-visibility sets in graphs

  Publication

  • M. Lemańska
  • M. Dettlaff
  • J. A. Rodriguez-Velazquez
  • I. G. Yero

  - ARS Mathematica Contemporanea - Year 2025

  Given a connected graph G, the mutual-visibility number of G is the cardinality of a largest set S such that for every pair of vertices x, y ∈ S there exists a shortest x, y-path whose interior vertices are not contained in S. Assume that a robot is assigned to each vertex of the set S. At each stage, one robot can move to a neighbouring vertex. Then S is a mobile mutual-visibility set of G if there exists a sequence of moves of...

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Year 2016

• Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring

  Publication

  • H. Furmańczyk
  • M. Kubale

  - ARS Mathematica Contemporanea - Year 2016

  A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...

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