ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Mathematicae Graph Theory 22(2) (2002) 361DOI: 10.7151/dmgt.1181
Faculty of Applied Mathematics
University of Mining and Metallurgy AGH
al. Mickiewicza 30, 30-059 Kraków, Poland
Let p and t stand for positive integers. Let R denote an edge subset of size |R| = (p2) mod t in the complete graph Kp. Call R a remainder (or
an edge t-remainder) in the clique Kp.
Conjecture L (L reminds of floor symbol). The floor class ⎣Kp/t⎦ is nonempty. In other words, there exists a graph F such that, for each edge
t-remainder R in Kp, F is a tth part of Kp−R, i.e., F ∈ ⎣Kp/t⎦.
Conjecture L implies the following conjecture stated in .
Conjecture L*. For each edge t-remainder R in Kp, there is an FR ∈ (Kp−R)/t = :⎣Kp/t⎦R.
Theorem L′ (Skupień ). There exists an edge
t-remainder R in Kp such that the floor class ⎣Kp/t⎦R is nonempty.
Plantholt's theorem  on chromatic index is equivalent to the truth of Conjecture L with t = p−1 and p being odd.
Conjecture L can be seen true for many pairs p, t, e.g., if t ≥ p−1 or t is small: t ≤ 5. If t
is a constant (t ≥ 4), both Conjectures can be reduced to some values of p in the
interval t+2 ≤ p ≤ 4t−5.
Received 28 November 2001