Errata for:
Carol T. Zamfirescu
(2)-pancyclic graphs
Discrete Appl. Math. 161, Iss. 7–8 (2013) 1128–1136
Concerning the proof of Theorem 4, two remarks are in order.
The case of a chord not intersected by any other chord is missing. Let p
be such a chord. There are two cycles using p and no other chord.
Furthermore, for each chord q \ne p there is a cycle using p and q and no
other chord. So we have c(p) \ge k + 1.
By Lemma 1 there exist intersecting chords s and t. Now there certainly is
a cycle using as chords p, s, and t, whence, c(p) \ge k + 2.
The statement "First of all, q halves G, and each half has as boundary a
cycle containing q; hence, c(q) \le 2n - 6." is false. We use the
following argument instead. q is not contained in C. Furthermore, G
contains at least three chords q, s, and t. q is not contained in the
cycle having as chords only s and t. So c(q) \le 2n - 6. Now the proof
continues as published.
In the proof of Theorem 5, consider the situation \mu(G) = 5, see Fig 5.
In the case where two nonconsecutive x_i vanish, there are in fact three
4-cycles, not one as stated in the article.
The above remarks do not change the validity of the statements.
Unforunately, there is a fundamental problem in Theorem 6 and its
Corollary. This will be addressed soon here.
My thanks go to Mr Matthias Kotz for pointing these out.