http://hdl.handle.net/1765/7874
series: EI 2006-23

# The induced path function, monotonicity and betweenness

### Changat, M. Mathew, J. Mulder, H.M.

Research Paper
This publication is part of collection
Related Files

(ei2006-23.pdf, 0.2MB)

(Article version.url.txt, 32 bytes)

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.

Keywords

Automatically Extracted Terms
• function
• graph
• transit
• transit function
• axiom
• path function
• vertex
• betweennes
• cycle
• path function j
• graph g
• vertice
• lemma
• transit functions
• transit function j
• transit axioms
• interval
• convexity
• v-path
• subgraph