Geodesic
Hamiltonian colorings of graphs with long cycles
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 263-275

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By a hamiltonian coloring of a connected graph $G$ of order $n \ge 1$ we mean a mapping $c$ of $V(G)$ into the set of all positive integers such that $\vert c(x) - c(y)\vert \ge n - 1 - D_G(x, y)$ (where $D_G(x, y)$ denotes the length of a longest $x-y$ path in $G$) for all distinct $x, y \in G$. In this paper we study hamiltonian colorings of non-hamiltonian connected graphs with long cycles, mainly of connected graphs of order $n \ge 5$ with circumference $n - 2$.
By a hamiltonian coloring of a connected graph $G$ of order $n \ge 1$ we mean a mapping $c$ of $V(G)$ into the set of all positive integers such that $\vert c(x) - c(y)\vert \ge n - 1 - D_G(x, y)$ (where $D_G(x, y)$ denotes the length of a longest $x-y$ path in $G$) for all distinct $x, y \in G$. In this paper we study hamiltonian colorings of non-hamiltonian connected graphs with long cycles, mainly of connected graphs of order $n \ge 5$ with circumference $n - 2$.
DOI : 10.21136/MB.2003.134180
Classification : 05C15, 05C38, 05C45, 05C78
Keywords: connected graphs; hamiltonian colorings; circumference 
Nebeský, Ladislav. Hamiltonian colorings of graphs with long cycles. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 263-275. doi: 10.21136/MB.2003.134180
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[2] G. Chartrand, L. Nebeský, P. Zhang: Hamiltonian colorings of graphs. Preprint (2001). | MR

[3] G. Chartrand, L. Nebeský, P. Zhang: On hamiltonian colorings of graphs. Preprint (2001). | MR

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