Quasiray decomposition of infinite graphs

Author
I. V. Protasov
Faculty of Cybernetics, Kyiv National University
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.
Keywords
infinite connected graph , set of vertices , subset, quasiray decomposition, partition an infinite group, countably many large subsets
DOI
doi:10.30970/ms.17.2.220-222
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
Volume
17
Issue
2
Year
2002
Journal
Matematychni Studii
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