The induced path function, monotonicity and betweenness
2006-06-28
Research Paper
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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
