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Proper-walk connection of hamiltonian digraphs.
- Source :
-
Applied Mathematics & Computation . Aug2022, Vol. 427, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- • We disprove a conjecture proposed by Fiedorowicz, Sidorowicz, Sopena (Appl. Math. Comput. 410 (2021) 126253). • In addition, we find a result of the above paper is not correct. • Two sufficient conditions are given for a hamiltonian digraph D with w c → (D) = 2. Under an arc-coloring c of a digraph D , if for each pair of vertices (u , v) , there exists a directed walk from u to v satisfying that any two consecutive arcs of it have different colors, we say that D is properly-walk connected, and c is a proper-walk coloring of D. The proper-walk connection number w c → (D) of D is the least integer k such that D has a proper-walk coloring with k colors. Fiedorowicz, Sidorowicz, Sopena (Appl. Math. Comput. 410 (2021) 126253) conjectured that if D is a hamiltonian digraph with δ (D) ≥ 2 , then w c → (D) ≤ 2. In this paper, we disprove the conjecture by constructing two families of counterexamples. Also, we present some cases for a hamiltonian digraph D having w c → (D) = 2. In addition, we find that Observation 15 is not true in the same paper. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIRECTED graphs
*RANDOM walks
*LOGICAL prediction
*INTEGERS
*MATHEMATICS
*COLORS
Subjects
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 427
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 156857991
- Full Text :
- https://doi.org/10.1016/j.amc.2022.127169