Browsing Research Articles (Mathematics and Applied Mathematics) by UP Author "Broere, Izak"

Browsing Research Articles (Mathematics and Applied Mathematics) by UP Author "Broere, Izak"

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  • Applications of Hajos-type constructions to the Hedetniemi conjecture 
    Broere, Izak; Matsoha, Moroli David Vusi (Wiley, 2017-06)
    Please read abstract in the article.
  • Asymmetric colorings of products of graphs and digraphs 
    Broere, Izak; Imrich, Wilfried; Kalinowski, Rafal; Pilśniak, Monika (Elsevier, 2019-08)
    We extend results about asymmetric colorings of finite Cartesian products of graphs to strong and direct products of graphs and digraphs. On the way we shorten proofs for the existence of prime factorizations of finite ...
  • Congruences and Hoehnke radicals on graphs 
    Broere, Izak; Heidema, Johannes; Veldsman, Stefan (Sciendo, 2020)
    We motivate, introduce, and study radicals on classes of graphs. This concept, and the theory which is developed, imitates the original notion of a Hoehnke radical in universal algebra using congruences. It is shown how ...
  • Constructing universal graphs for induced-hereditary graph properties 
    Broere, Izak; Heidema, Johannes; Mihok, Peter (Springer, 2013-04)
    Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m'th position of its binary expansion. ...
  • The distinguishing index of infinite graphs 
    Broere, Izak; Pilsniak, Monika (Australian National University, Research School of Computer Science, 2015-03-30)
    The distinguishing index D0(G) of a graph G is the least cardinal d such that G has an edge colouring with d colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing ...
  • The distinguishing index of the Cartesian product of countable graphs 
    Broere, Izak; Pilsniak, Monika (University of Primorska, Slovenia , Society of Mathematicians, Physicists and Astronomers of Slovenia and the Institute of Mathematics, Physics and Mechanics in Ljubljana, 2017)
    Please read abstract in the article.
  • Graph congruences and what they connote 
    Broere, Izak; Heidema, Johannes; Pretorius, Lou (Taylor and Francis, 2018)
    Please read abstract in the article.
  • Hamiltonicity and generalised total colourings of planar graphs 
    Borowiecki, Mieczyslaw; Broere, Izak (De Gruyter Open, 2016)
    The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph ...
  • Moment balancing templates for (d, k) - constrained codes and run-length limited sequences 
    Cheng, Ling; Ferreira, Hendrik Christoffel; Broere, Izak (IEEE Information Theory Society, 2012-04)
    The first-order moment of (d, k) -constrained codes is investigated in this paper. A generalized moment balancing template is proposed to encode a (d, k) sequence into a single insertion of deletion correcting codeword ...
  • The property of k-colourable graphs is uniquely decomposable 
    Broere, Izak; Dorfling, Michael J. (Elsevier, 2013-10)
    An additive hereditary graph property is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If P1; : : : ;Pn are graph properties, then a (P1; : : : ;Pn)-decomposition of a graph G is a ...
  • The quest for a characterization of hom-properties of finite character 
    Broere, Izak; Matsoha, Moroli D.V.; Heiema, Johannes (De Gruyter Open, 2016)
    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 ...
  • Some bounds on the generalised total chromatic number of degenerate graphs 
    Broere, Izak; Semanišin, Gabriel (Elsevier, 2017-06)
    The total generalised colourings considered in this paper are colourings of the vertices and of the edges of graphs satisfying the following conditions: • each set of vertices of the graph which receive the same colour ...
  • Unique factorization of compositive hereditary graph properties 
    Broere, Izak; Drgas-Burchardt, Ewa (Springer, 2012-02)
    Please read abstract in article.
  • Universal H-colourable graphs 
    Broere, Izak; Heidema, Johannes (Springer, 2013)
    Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: for given m and n with m < n, m is adjacent to n if n has a 1 in the mth position of its binary expansion. ...
  • Universality for and in induced-hereditary graph properties 
    Broere, Izak; Heidema, Johannes (2013)
    The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 20 pairwise non-isomorphic ...
  • Universality in graph properties allowing constrained growth 
    Broere, Izak; Heidema, Johannes (Elsevier, 2020)
    A graph property is a class of graphs which is closed under isomorphisms. Some properties are also closed under one or more specified constructions that extend any graph into a supergraph containing the original graph as ...