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TRAVERSING A GRAPH IN GENERAL POSITION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 3 / December 2023
- Published online by Cambridge University Press:
- 13 February 2023, pp. 353-365
- Print publication:
- December 2023
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- Article
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Let G be a graph. Assume that to each vertex of a set of vertices
$S\subseteq V(G)$ a robot is assigned. At each stage one robot can move to a neighbouring vertex. Then S is a mobile general position set of G if there exists a sequence of moves of the robots such that all the vertices of G are visited while maintaining the general position property at all times. The mobile general position number of G is the cardinality of a largest mobile general position set of G. We give bounds on the mobile general position number and determine exact values for certain common classes of graphs, including block graphs, rooted products, unicyclic graphs, Kneser graphs 
$K(n,2)$ and line graphs of complete graphs.
