Please use this identifier to cite or link to this item: http://hdl.handle.net/10263/7307
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dc.contributor.authorPatle, Prajyot Subhash-
dc.date.accessioned2022-03-24T05:57:14Z-
dc.date.available2022-03-24T05:57:14Z-
dc.date.issued2021-07-
dc.identifier.citation21p.en_US
dc.identifier.urihttp://hdl.handle.net/10263/7307-
dc.descriptionDissertation under the supervision of Mathew C. Francisen_US
dc.description.abstractExtremal graphs are graphs which sit at the extremes. In simpler words for a class of graphs which satisfy a certain property, extremal graphs are the ones which exhibit a minimum or maximum of that property. Here, we take a look at a property which is exhibited by any graph in general; δα ≤ ∆µ, where δ is the minimum degree of the graph, α is the size of the maximum independent set, ∆ is the maximum degree, and µ is the size of the maximum matching of the graph. We first look at non-regular extremal graphs and regular extremal graphs (with degree 2 and 3) with respect to the above property as characterized by Mohr and Rautenbach. Later we try our hand at characterizing the regular extremal graphs using a general graph decomposition given jointly by Edmonds and Gallai. In doing so, we obtain a new proof for Mohr and Rautenbach’s characterization of 3-regular extremal graphs and we believe our approach can be easily adapted to characterize k-regular extremal graphs for values of k ≥ 3.en_US
dc.language.isoenen_US
dc.publisherIndian Statistical Institute, Kolkata.en_US
dc.relation.ispartofseriesDissertation;CS-1927-
dc.subjectExtremal graphsen_US
dc.subjectGallai-Edmonds Decompositionen_US
dc.subjectNon-regular Extremal Graphs .en_US
dc.subjectRegular Extremal Graphs .en_US
dc.titleGraphs with equal independence and matching numberen_US
dc.typeOtheren_US
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