A forbidden subgraph characterization of some graph classes using betweenness axioms

Changat, Manoj; Lakshmikuttyamma, Anandavally K.; Mathews, J. Howard; Peterin, Iztok; Narasimha-Shenoi, Prasanth G.; Seethakuttyamma, Geetha; Špacapan, Simon

doi:10.1016/j.disc.2013.01.013

Cited by 15 publications

(9 citation statements)

References 11 publications

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“…Theorem 2. [4] For every graph G, I G satisfies the (J3) axiom if and only if G is HHP 3 -fanfree graph.…”

Section: Interval Function Of Distance Hereditary Graphsmentioning

confidence: 99%

“…We provide examples in the respective sections for the independence of the axioms (J2 ′ ) and (J3 ′ ) and (J0 ′ ). The axioms (J2 ′ ) and (J3 ′ ) were first considered in [6] and later in [4]. The axiom (J0) first appeared in [24] for characterizing the interval function of trees.…”

Section: Introductionmentioning

confidence: 99%

“…The axiom (J0) first appeared in [24] for characterizing the interval function of trees. The axiom is discussed in [4] for characterizing the interval function of a Ptolemaic graph G. We may observe that both the family of bridged graphs BG and distance hereditary graphs DH is a strict super class of the family of Ptolemaic graphs,PG, that is, PG DH and PG BG and BG and DH coincide only in PG. But, BG DH and DH BG, This relation is also reflected in the implications between the axioms (J0), (J2 ′ ), (J3 ′ ) and (J0 ′ ).…”

Section: Introductionmentioning

confidence: 99%

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The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations

Changat,

Sheela,

Narasimha-Shenoi

2020

Preprint

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In this paper we consider certain types of betweenness axioms on the interval function I G of a connected graph G. We characterize the class of graphs for which I G satisfy these axioms. The class of graphs that we characterize include the important class of Ptolemaic graphs and some proper superclasses of Ptolemaic graphs: the distance hereditary graphs and the bridged graphs.We also provide axiomatic characterizations of the interval function of these classes of graphs using an arbitrary function known as transit function.

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“…Theorem 2. [4] For every graph G, I G satisfies the (J3) axiom if and only if G is HHP 3 -fanfree graph.…”

Section: Interval Function Of Distance Hereditary Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations

Changat,

Sheela,

Narasimha-Shenoi

2020

Preprint

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“…This axiom was called axiom (J0) in [4]. In Section 4 we will see that our four betweenness axioms do not imply axiom (Υ ).…”

Section: Example 4 (A Betweenness R That Does Not Satisfymentioning

confidence: 99%

“…In [17] a unifying approach for moving around in discrete structures such as graphs and partially ordered sets was presented: a transit function R : V × V → 2 V satisfying three elementary axioms. It includes all of the above functions, but also other so-called path functions, like the induced path function J, see [6,7], where J(u, v) consists of the vertices on induced paths between u and v. Recently in [4] characterizations of some graph classes were obtained using betweenness axioms on the interval function and on the induced path function.…”

Section: Introductionmentioning

confidence: 98%

Axiomatic characterization of the interval function of a block graph

Balakrishnan

Changat

Lakshmikuttyamma³

et al. 2015

Discrete Mathematics

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a b s t r a c tIn 1952 Sholander formulated an axiomatic characterization of the interval function of a tree with a partial proof. In 2011 Chvátal et al. gave a completion of this proof. In this paper we present a characterization of the interval function of a block graph using axioms on an arbitrary transit function R. From this we deduce two new characterizations of the interval function of a tree.

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