Achromatic number of K 5 × K n for small n

Mirko Horňák; Štefan Pčola

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 4, page 963-988
  • ISSN: 0011-4642

Abstract

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The achromatic number of a graph G is the maximum number of colours in a proper vertex colouring of G such that for any two distinct colours there is an edge of G incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of K 5 and K n for all n ≤ 24 .

How to cite

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Horňák, Mirko, and Pčola, Štefan. "Achromatic number of $K_5 \times K_n$ for small $n$." Czechoslovak Mathematical Journal 53.4 (2003): 963-988. <http://eudml.org/doc/30828>.

@article{Horňák2003,
abstract = {The achromatic number of a graph $G$ is the maximum number of colours in a proper vertex colouring of $G$ such that for any two distinct colours there is an edge of $G$ incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of $K_5$ and $K_n$ for all $n \le 24$.},
author = {Horňák, Mirko, Pčola, Štefan},
journal = {Czechoslovak Mathematical Journal},
keywords = {complete vertex colouring; achromatic number; Cartesian product; complete graph; complete vertex colouring; achromatic number; Cartesian product; complete graph},
language = {eng},
number = {4},
pages = {963-988},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Achromatic number of $K_5 \times K_n$ for small $n$},
url = {http://eudml.org/doc/30828},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Horňák, Mirko
AU - Pčola, Štefan
TI - Achromatic number of $K_5 \times K_n$ for small $n$
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 963
EP - 988
AB - The achromatic number of a graph $G$ is the maximum number of colours in a proper vertex colouring of $G$ such that for any two distinct colours there is an edge of $G$ incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of $K_5$ and $K_n$ for all $n \le 24$.
LA - eng
KW - complete vertex colouring; achromatic number; Cartesian product; complete graph; complete vertex colouring; achromatic number; Cartesian product; complete graph
UR - http://eudml.org/doc/30828
ER -

References

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  1. Indice achromatique des graphes multiparti complets et réguliers, Cahiers Centre Études Rech. Opér. 20 (1978), 331–340. (1978) Zbl0404.05026MR0543176
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  4. The harmonious chromatic number and the achromatic number, In: Surveys in Combinatorics 1997. London Math. Soc. Lect. Notes Series 241, R. A. Bailey (ed.), Cambridge University Press, 1997, pp. 13–47. (1997) Zbl0882.05062MR1477743
  5. An interpolation theorem for graphical homomorphisms, Portug. Math. 26 (1967), 454–462. (1967) MR0272662
  6. 10.1016/S0012-365X(00)00399-X, Discrete Math. 234 (2001), 159–169. (2001) MR1826830DOI10.1016/S0012-365X(00)00399-X
  7. On the achromatic number of K m × K n , In: Graphs and Other Combinatorial Topics. Proceedings of the Third Czechoslovak Symposium on Graph Theory, Prague, August 24–27, 1982, M.  Fiedler (ed.), Teubner, Leipzig, 1983, pp. 118–123. (1983) MR0737024
  8. 10.1137/0138030, SIAM J.  Appl. Math. 38 (1980), 364–372. (1980) MR0579424DOI10.1137/0138030

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