Achromatic number of $K_5 \times K_n$ for small $n$

Mirko Horňák; Štefan Pčola

Achromatic number of $K_{5} \times K_{n}$ for small $n$

Mirko Horňák; Štefan Pčola

Czechoslovak Mathematical Journal (2003)

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

Access Full Article

top

Access to full text

Full (PDF)

Abstract

top

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 \leq 24

.

How to cite

top

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

top

Indice achromatique des graphes multiparti complets et réguliers, Cahiers Centre Études Rech. Opér. 20 (1978), 331–340. (1978) Zbl0404.05026 MR0543176
On the achromatic number of the Cartesian product $G_{1} \times G_{2}$ , Australas. J. Combin. 6 (1992), 111–117. (1992) MR1196112
10.1016/0012-365X(93)E0207-K, Discrete Math. 141 (1995), 61–66. (1995) MR1336673 DOI10.1016/0012-365X(93)E0207-K
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) Zbl0882.05062 MR1477743
An interpolation theorem for graphical homomorphisms, Portug. Math. 26 (1967), 454–462. (1967) MR0272662
10.1016/S0012-365X(00)00399-X, Discrete Math. 234 (2001), 159–169. (2001) MR1826830 DOI10.1016/S0012-365X(00)00399-X
On the achromatic number of $K_{m} \times K_{n}$ , 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
10.1137/0138030, SIAM J. Appl. Math. 38 (1980), 364–372. (1980) MR0579424 DOI10.1137/0138030

NotesEmbed ?

top

You must be logged in to post comments.