Quasiray decomposition of infinite graphs |
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| Author |
Faculty of Cybernetics, Kyiv National University
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| Abstract |
Let $\mathop{\rm Gr}$ be an infinite connected graph with a set of vertices
${ V}.$ A subset $Q\subseteq { V}$ is called a~quasiray if
there exists a bijection $f\colon w\to { V}$ such that
$d(f(i), f(i+1))\leq 3$ for every $i\in w$, where $d$ is a path
metric on ${ V}$. A quasiray decomposition is applied to
partition an infinite group into countably many large subsets.
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| Keywords |
infinite connected graph , set of vertices , subset, quasiray decomposition, partition an infinite group, countably many large subsets
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| DOI |
doi:10.30970/ms.17.2.220-222
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Reference |
1. Protasov I. V. Morphisms of ball's structures of groups anf graphs, Ukr. Matem. Zhurn. 53 (2002), № 6.
2. Ore O. Theory of graphs, Amer. Math. Soc. Colloquium Publications, Vol. XXXVIII, 1962. 3. Bella A., Malykhin V. I. Small and others subsets of a group, Q and A in General Topology 11 (1999), 183–187. |
| Pages |
220-222
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| Volume |
17
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| Issue |
2
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| Year |
2002
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| Journal |
Matematychni Studii
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| Full text of paper | |
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