Induced path transit function, monotone and Peano axioms
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- 作者：Changat ; Manoj ; Mathew ; Joseph
- 关键词：Transit function ; Induced path ; Monotone axiom ; Peano axiom ; JHC convexity
- 刊名：Discrete Mathematics
- 出版年：2004
- 出版时间：September 28, 2004
- 年：2004
- 卷：286
- 期：3
- 页码：185-194
- 全文大小：478 K
文摘
The induced path transit function J(u,v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v. A transit function J satisfies monotone axiom if x,y
J(u,v) implies J(x,y)
J(u,v). A transit function J is said to satisfy the Peano axiom if, for any u,v,wV,xJ(v,w), yJ(u,x), there is a zJ(u,v) such that yJ(w,z). These two axioms are equivalent for the induced path transit function of a graph. Planar graphs for which the induced path transit function satisfies the monotone axiom are characterized by forbidden induced subgraphs.
J(u,v) implies J(x,y)J(u,v). A transit function J is said to satisfy the Peano axiom if, for any u,v,wV,xJ(v,w), yJ(u,x), there is a zJ(u,v) such that yJ(w,z). These two axioms are equivalent for the induced path transit function of a graph. Planar graphs for which the induced path transit function satisfies the monotone axiom are characterized by forbidden induced subgraphs.