n-arc and n-circle connected graph-like spaces

Abstract

A space X is n-arc connected (respectively, n-circle connected) if for any choice of at most n points there is an arc (respectively, a circle) in X containing the specified points. We study n-arc connectedness and n-circle connectedness in compactifications of locally finite graphs and the slightly more general class of graph-like continua, uncovering a striking difference in their behaviour regarding n-arc and -circle connectedness.2010 Mathematics Subject Classification. Primary: 05C63, 05C38. Secondary: 05C45, 54F15, 57M15.