Abstract
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Abstract
Keywords: sum-list colouring, acyclic colouring, grids, generalized Petersen graphs. 
Abstract
The correction of Lemma 5.18 consists in adding the assumption: there is no 4-vertex cycle that contains both v 1 , v 2 vertices.
Abstract
The change in the form of Lemma 5.18 has no consequences in the paper. The proof of the lemma and the application of the lemma are given under this assumption.
Abstract
Next we give the corrected version of the whole section "Concluding remarks". We substitute "n ≡" with "m ≡" in two equations describing G n,m and χ D1 sc (G n,m ), respectively. Moreover, the exact value G n,m given as a function of n, m, and consequently the lower bound on χ D1 sc (P n P m ) given in Corollary 6.1 are corrected (it was a calculating mistake).

1. CORRECTION OF LEMMA 5.18 OF [1] We present the following corrected version of Lemma 5.18. 

The correction of Lemma 5.18 consists in adding the assumption: there is no 4-vertex cycle that contains both v 1 , v 2 vertices.

The change in the form of Lemma 5.18 has no consequences in the paper. The proof of the lemma and the application of the lemma are given under this assumption.

Next we give the corrected version of the whole section "Concluding remarks". We substitute "n ≡" with "m ≡" in two equations describing G n,m and χ D1 sc (G n,m ), respectively. Moreover, the exact value G n,m given as a function of n, m, and consequently the lower bound on χ D1 sc (P n P m ) given in Corollary 6.1 are corrected (it was a calculating mistake). 
CONCLUDING REMARKS
Several supporting results presented in the paper can be used as tools for other research in this field. Some of them could help us to establish the exact values of χ D1 sc (P n P m ), when both n, m ≥ 5. We are able to calculate some special numbers of this type but, in general, Problem 5.3 is still open. The method that is used in this work when min{n, m} ≤ 4 fails in the possible analogue of Lemma 5.14.
CONCLUDING REMARKS
On the other hand, Theorem 5.21 implies the improvement of Corollary 5.1. Actually, graphs P n P m with n ≥ 1, m ≥ 4 contain subgraphs G n,m of the forms
CONCLUDING REMARKS
As we mentioned previously, χ
CONCLUDING REMARKS
Careful calculation of these numbers yields
CONCLUDING REMARKS
is an asymptotically better lower bound on χ D1 sc (P n P m ) than that one which was obtained in Corollary 5.1.
CONCLUDING REMARKS
We turn out Lemma 5.2 to write its two alternative statements by one inequality.
CONCLUDING REMARKS
Now we combine all the above observations and known values of χ D1 sc (P n P m ) that were discussed in the previous section in the following result. 

{'paper_id': '125692140', 'title': 'Corrigendum to "Acyclic sum-list-colouring of grids and other classes of graphs" [Opuscula Math. 37, no. 4 (2017), 535-556]', 's2_url': 'https://api.semanticscholar.org/CorpusID:125692140', 'source': 'S2ORC'}