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- W4224117510 abstract "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 wc→(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 wc→(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 wc→(D)=2. In addition, we find that Observation 15 is not true in the same paper." @default.
- W4224117510 created "2022-04-19" @default.
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- W4224117510 date "2022-08-01" @default.
- W4224117510 modified "2023-09-25" @default.
- W4224117510 title "Proper-walk connection of hamiltonian digraphs" @default.
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- W4224117510 doi "https://doi.org/10.1016/j.amc.2022.127169" @default.
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