Book ChapterDOI
Axiomatic Characterization of the Interval Function of a Bipartite Graph
Manoj Changat,Ferdoos Hossein Nezhad,N. Narayanan +2 more
- pp 96-106
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TLDR
A new axiom is introduced: for any x,y,z, R(x,y) = x, y = Rightarrow y in R (x,z) or x in R(y,Z) for any \( x,Y,z \in V\),Abstract:
The axiomatic approach with the interval function and induced path transit function of a connected graph is an interesting topic in metric and related graph theory. In this paper, we introduce a new axiom:
(bp) for any \( x,y,z \in V\), \(R(x,y)=\{x,y\} \Rightarrow y\in R(x,z)\) or \(x\in R(y,z)\).read more
Citations
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Journal ArticleDOI
Betweenness in graphs: A short survey on shortest and induced path betweenness
TL;DR: The results are surveyed as answers to these questions available from the research papers on the interval function of special graphs using some set of first order axioms defined on an arbitrary transit function.
Journal ArticleDOI
Interval function, induced path function, (claw, paw)-free graphs and axiomatic characterizations
TL;DR: This paper presents characterizations of (claw, paw)-free graphs using axiom (cp) on the standard path transit functions on graphs, namely the interval function, the induced path function, and the all-paths function.
Posted Content
The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations.
TL;DR: The class of graphs that are characterized include the important class of Ptolemaic graphs and some proper superclasses of P toleMAic graphs: the distance hereditary graphs and the bridged graphs.
References
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Journal ArticleDOI
Convex sets in graphs, II. Minimal path convexity
TL;DR: Caratheodory, Helly and Radon type theorems are proved for M-convex sets and the Helly number equals the size of a maximum clique.
Journal ArticleDOI
Trees, lattices, order, and betweenness
TL;DR: This paper considers postulates expressed in terms of "segments," "medians," and "betweenness" for trees, lattices, and partially ordered sets.
Journal ArticleDOI
Convexities related to path properties on graphs
TL;DR: This work proposes a more general approach for 'path properties' in graphs, focusing on the behaviour of such convexities on the Cartesian product of graphs and on the classical convexity invariants, such as the Caratheodory, Helly and Radon numbers in relation with graph invariants.
Journal ArticleDOI
Medians and betweenness
TL;DR: In this paper, it was shown that median lattices and trees have a common generalization and that median semilattices can be imbedded in distributive lattices.
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