Further results on Erdős–Faber–Lovász conjecture
In 1972, Erdős–Faber–Lovász (EFL) conjectured that, if is a linear hypergraph consisting of edges of cardinality , then it is possible to color the vertices with colors so that no two vertices with the same color are in the same edge. In 1978, Deza, Erdös and Frankl had given an equivalent version o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.03.003 |
| _version_ | 1818392199656636416 |
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| author | S.M. Hegde Suresh Dara |
| author_facet | S.M. Hegde Suresh Dara |
| author_sort | S.M. Hegde |
| collection | DOAJ |
| description | In 1972, Erdős–Faber–Lovász (EFL) conjectured that, if is a linear hypergraph consisting of edges of cardinality , then it is possible to color the vertices with colors so that no two vertices with the same color are in the same edge. In 1978, Deza, Erdös and Frankl had given an equivalent version of the same for graphs: Let denote a graph with complete graphs , each having exactly vertices and have the property that every pair of complete graphs has at most one common vertex, then the chromatic number of is . The clique degree of a vertex in is given by . In this paper we give a method for assigning colors to the graphs satisfying the hypothesis of the Erdős–Faber–Lovász conjecture and every () has atmost vertices of clique degree greater than one using Symmetric latin Squares and clique degrees of the vertices of . |
| first_indexed | 2024-12-14T05:25:37Z |
| format | Article |
| id | doaj.art-c2551f2022f141a4b2cb3503516de6e6 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-12-14T05:25:37Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-c2551f2022f141a4b2cb3503516de6e62022-12-21T23:15:32ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742020-01-0117161463110.1016/j.akcej.2019.03.0031760681Further results on Erdős–Faber–Lovász conjectureS.M. Hegde0Suresh Dara1Department of Mathematical and Computational Sciences, National Institute of Technology KarnatakaInstitute of Mathematical Sciences, HBNIIn 1972, Erdős–Faber–Lovász (EFL) conjectured that, if is a linear hypergraph consisting of edges of cardinality , then it is possible to color the vertices with colors so that no two vertices with the same color are in the same edge. In 1978, Deza, Erdös and Frankl had given an equivalent version of the same for graphs: Let denote a graph with complete graphs , each having exactly vertices and have the property that every pair of complete graphs has at most one common vertex, then the chromatic number of is . The clique degree of a vertex in is given by . In this paper we give a method for assigning colors to the graphs satisfying the hypothesis of the Erdős–Faber–Lovász conjecture and every () has atmost vertices of clique degree greater than one using Symmetric latin Squares and clique degrees of the vertices of .http://dx.doi.org/10.1016/j.akcej.2019.03.003chromatic numbererdős–faber–lovász conjecturesymmetric latin square |
| spellingShingle | S.M. Hegde Suresh Dara Further results on Erdős–Faber–Lovász conjecture AKCE International Journal of Graphs and Combinatorics chromatic number erdős–faber–lovász conjecture symmetric latin square |
| title | Further results on Erdős–Faber–Lovász conjecture |
| title_full | Further results on Erdős–Faber–Lovász conjecture |
| title_fullStr | Further results on Erdős–Faber–Lovász conjecture |
| title_full_unstemmed | Further results on Erdős–Faber–Lovász conjecture |
| title_short | Further results on Erdős–Faber–Lovász conjecture |
| title_sort | further results on erdos faber lovasz conjecture |
| topic | chromatic number erdős–faber–lovász conjecture symmetric latin square |
| url | http://dx.doi.org/10.1016/j.akcej.2019.03.003 |
| work_keys_str_mv | AT smhegde furtherresultsonerdosfaberlovaszconjecture AT sureshdara furtherresultsonerdosfaberlovaszconjecture |