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Start Over Creator Polat, Norbert

1. End-faithful spanning trees of countable graphs with prescribed sets of rays

Creator:
Polat, Norbert
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math, countable graphs, and prescribed sets of rays
Language:
English
Description:
We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Multi-faithful spanning trees of infinite graphs

Creator:
Polat, Norbert
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
infinite graph, end, end-faithful, spanning tree, and multiplicity
Language:
English
Description:
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 tm}(\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 $\mathop {\mathrm tm}(\tau ) \le f(\tau ) \le m(\tau )$, there exists a spanning tree $T$ of $G$ such that $m_{T}(\tau ) = f(\tau )$ for every end $\tau $ of $G$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public