Convexity in Helly Graphs: Selection and Almost Fixed Point Properties for Multifunctions
Copyright policy )Convexity in Helly Graphs: Selection and Almost Fixed Point Properties for Multifunctions
AbstractIn this paper, a notion of convexity structure for graphs, called neighbourhood convexity, is introduced. It is shown that neighbourhood convexity is exactly the graph convexity for Helly graphs to be 2-Helly. We then consider various neighbourhood-convexity almost fixed point properties for Helly graphs. In particular, we show that for any positive number p, every Helly graph has the neighbourhood convexity ⌈p2⌉-almost fixed point property for p-weak multifunctions; and any self-mapping neighbourhood convexity strong multifunction has a selection.
- Imperial College London United Kingdom
Almost fixed point property, Graph convexity, Multifunctions, Fixed clique property, Selection property, Helly graphs, Theoretical Computer Science, Computer Science(all)
Almost fixed point property, Graph convexity, Multifunctions, Fixed clique property, Selection property, Helly graphs, Theoretical Computer Science, Computer Science(all)
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