On the heterochromatic number of circulant digraphs

• Autorzy: Hortensia Galeana-Sánchez , Víctor Neumann-Lara
• Języki publikacji: EN

Abstrakty

EN

The heterochromatic number hc(D) of a digraph D, is the minimum integer k such that for every partition of V(D) into k classes, there is a cyclic triangle whose three vertices belong to different classes.
For any two integers s and n with 1 ≤ s ≤ n, let $D_{n,s}$ be the oriented graph such that $V(D_{n,s})$ is the set of integers mod 2n+1 and $A(D_{n,s}) = {(i,j) : j-i ∈ {1,2,...,n}∖{s}}..
In this paper we prove that $hc(D_{n,s}) ≤ 5$ for n ≥ 7. The bound is tight since equality holds when s ∈ {n,[(2n+1)/3]}.

Słowa kluczowe

EN

circulant tournament; vertex colouring; heterochromatic number; heterochromatic triangle

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 73-79

Daty

wydano

2004

otrzymano

2001-06-29

poprawiono

2003-05-13

Twórcy

autor

Hortensia Galeana-Sánchez

• Instituto de Matemáticas, UNAM, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F., MÉXICO

autor

Víctor Neumann-Lara

• Instituto de Matemáticas, UNAM, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F., MÉXICO

Bibliografia

• [1] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1973).
• [2] B. Abrego, J.L. Arocha, S. Fernández Merchant and V. Neumann-Lara, Tightness problems in the plane, Discrete Math. 194 (1999) 1-11, doi: 10.1016/S0012-365X(98)00031-4.
• [3] J.L. Arocha, J. Bracho and V. Neumann-Lara, On the minimum size of tight hypergraphs, J. Graph Theory 16 (1992) 319-326, doi: 10.1002/jgt.3190160405.
• [4] P. Erdős, M. Simonovits and V.T. Sós, Anti-Ramsey Theorems (in: Infinite and Finite Sets, Keszthely, Hungary, 1973), Colloquia Mathematica Societatis János Bolyai 10 633-643.
• [5] H. Galeana-Sánchez and V. Neumann-Lara, A class of tight circulant tournaments, Discuss. Math. Graph Theory 20 (2000) 109-128, doi: 10.7151/dmgt.1111.
• [6] Y. Manoussakis, M. Spyratos, Zs. Tuza, M. Voigt, Minimal colorings for properly colored subgraphs, Graphs and Combinatorics 12 (1996) 345-360, doi: 10.1007/BF01858468.
• [7] V. Neumann-Lara, The acyclic disconnection of a digraph, Discrete Math. 197-198 (1999) 617-632.

Identyfikatory

DOI

10.7151/dmgt.1214