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The induced path function, monotonicity and betweenness

Author

Listed:
  • Changat, M.
  • Mathew, J.
  • Mulder, H.M.

Abstract

The induced path function $J(u, v)$ of a graph consists of the set of all vertices lying on the induced paths between vertices $u$ and $v$. This function is a special instance of a transit function. The function $J$ satisfies betweenness if $w \\in J(u, v)$ implies $u \\notin J(w, v)$ and $x \\in J(u, v)$ implies $J(u, x \\subseteq J(u, v)$, and it is monotone if $x, y \\in J(u, v)$ implies $J(x, y) \\subseteq J(u, v)$. The induced path function of a connected graph satisfying the betweenness and monotone axioms are characterized by transit axioms.

Suggested Citation

  • Changat, M. & Mathew, J. & Mulder, H.M., 2006. "The induced path function, monotonicity and betweenness," Econometric Institute Research Papers EI 2006-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:7874
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    Cited by:

    1. Mulder, H.M., 2007. "Transit functions on graphs (and posets)," Econometric Institute Research Papers EI 2007-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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