I.A.E., Universite Jean Moulin (Lyon 3), 6 cours Albert Thomas, 69355 Lyon Cedex 08, France, e-mail: polat@jonas.univ-lyon1.fr
Abstract: For an end $\tau$ and a tree $T$ of a graph $G$ we denote respectively by $m(\tau)$ and $m_T(\tau)$ the maximum numbers of pairwise disjoint rays of $G$ and $T$ belonging to $\tau$, and we define $\tm(\tau) := \min\{m_T(\tau) T \text{ is a spanning tree of } G \}$. In this paper we give partial answers - affirmative and negative ones - to the general problem of determining if, for a function $f$ mapping every end $\tau$ of $G$ to a cardinal $f(\tau)$ such that $\tm(\tau) \leq f(\tau) \leq m(\tau)$, there exists a spanning tree $T$ of $G$ such that $m_T(\tau) = f(\tau)$ for every end $\tau$ of $G$.
Keywords: infinite graph, end, end-faithful, spanning tree, multiplicity
Classification (MSC 2000): 05C99
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