Multi-faithful spanning trees of infinite graphs

Polat, Norbert. "Multi-faithful spanning trees of infinite graphs." Czechoslovak Mathematical Journal 51.3 (2001): 477-492. <http://eudml.org/doc/30650>.

@article{Polat2001,
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 $\mathop \{\mathrm \{t\}m\}(\tau ) := \min \lbrace m_\{T\}(\tau )\: T \text\{is\} \text\{a\} \text\{spanning\} \text\{tree\} \text\{of\} G \rbrace $. 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 $\mathop \{\mathrm \{t\}m\}(\tau ) \le f(\tau ) \le m(\tau )$, there exists a spanning tree $T$ of $G$ such that $m_\{T\}(\tau ) = f(\tau )$ for every end $\tau $ of $G$.},
author = {Polat, Norbert},
journal = {Czechoslovak Mathematical Journal},
keywords = {infinite graph; end; end-faithful; spanning tree; multiplicity; infinite graph; end; end-faithful; spanning tree; multiplicity},
language = {eng},
number = {3},
pages = {477-492},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multi-faithful spanning trees of infinite graphs},
url = {http://eudml.org/doc/30650},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Polat, Norbert
TI - Multi-faithful spanning trees of infinite graphs
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 477
EP - 492
AB - 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 $\mathop {\mathrm {t}m}(\tau ) := \min \lbrace m_{T}(\tau )\: T \text{is} \text{a} \text{spanning} \text{tree} \text{of} G \rbrace $. 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 $\mathop {\mathrm {t}m}(\tau ) \le f(\tau ) \le m(\tau )$, there exists a spanning tree $T$ of $G$ such that $m_{T}(\tau ) = f(\tau )$ for every end $\tau $ of $G$.
LA - eng
KW - infinite graph; end; end-faithful; spanning tree; multiplicity; infinite graph; end; end-faithful; spanning tree; multiplicity
UR - http://eudml.org/doc/30650
ER -