TY - JOUR
T1 - Achromatic number versus pseudoachromatic number
T2 - A counterexample to a conjecture of Hedetniemi
AU - Edwards, Keith J.
N1 - Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2000/5/28
Y1 - 2000/5/28
N2 - The pseudoachromatic number of a graph is the largest number of colours in a (not necessarily proper) vertex colouring of the graph such that every pair of distinct colours appears on the endpoints of some edge. The achromatic number is largest number of colours which can be used if the colouring must also be proper. Hedetniemi (http://cyclone.cs.clemson.edu/~hedet/coloring.html) conjectured that these two parameters are equal for all trees. We disprove this conjecture by giving an infinite family of trees for which the pseudoachromatic number strictly exceeds the achromatic number.
AB - The pseudoachromatic number of a graph is the largest number of colours in a (not necessarily proper) vertex colouring of the graph such that every pair of distinct colours appears on the endpoints of some edge. The achromatic number is largest number of colours which can be used if the colouring must also be proper. Hedetniemi (http://cyclone.cs.clemson.edu/~hedet/coloring.html) conjectured that these two parameters are equal for all trees. We disprove this conjecture by giving an infinite family of trees for which the pseudoachromatic number strictly exceeds the achromatic number.
UR - http://www.scopus.com/inward/record.url?scp=0347646985&partnerID=8YFLogxK
U2 - 10.1016/S0012-365X(00)00025-X
DO - 10.1016/S0012-365X(00)00025-X
M3 - Article
AN - SCOPUS:0347646985
SN - 0012-365X
VL - 219
SP - 271
EP - 274
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -