Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number...
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| Format: | Article |
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University of Zielona Góra
2019-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2096 |
| _version_ | 1797713160440905728 |
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| author | Volkmann Lutz |
| author_facet | Volkmann Lutz |
| author_sort | Volkmann Lutz |
| collection | DOAJ |
| description | Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017. |
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| format | Article |
| id | doaj.art-9a2b088d6ca14988b89262f3e1e33a63 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:06Z |
| publishDate | 2019-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-9a2b088d6ca14988b89262f3e1e33a632023-09-02T21:43:06ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922019-05-0139256757310.7151/dmgt.2096dmgt.2096Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique NumberVolkmann Lutz0Lehrstuhl II für Mathematik, RWTH Aachen University, 52056Aachen, GermanyLet G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.https://doi.org/10.7151/dmgt.2096edge-connectivityclique numbermaximally edge-connected graphssuper-edge-connected graphs05c40 |
| spellingShingle | Volkmann Lutz Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number Discussiones Mathematicae Graph Theory edge-connectivity clique number maximally edge-connected graphs super-edge-connected graphs 05c40 |
| title | Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number |
| title_full | Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number |
| title_fullStr | Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number |
| title_full_unstemmed | Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number |
| title_short | Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number |
| title_sort | sufficient conditions for maximally edge connected and super edge connected graphs depending on the clique number |
| topic | edge-connectivity clique number maximally edge-connected graphs super-edge-connected graphs 05c40 |
| url | https://doi.org/10.7151/dmgt.2096 |
| work_keys_str_mv | AT volkmannlutz sufficientconditionsformaximallyedgeconnectedandsuperedgeconnectedgraphsdependingonthecliquenumber |