On Graphs Representable by Pattern-Avoiding Words
In this paper we study graphs defined by pattern-avoiding words. Word-representable graphs have been studied extensively following their introduction in 2004 and are the subject of a book published by Kitaev and Lozin in 2015. Recently there has been interest in studying graphs represented by patter...
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| Format: | Article |
| Language: | English |
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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.2128 |
| _version_ | 1827844647131545600 |
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| author | Mandelshtam Yelena |
| author_facet | Mandelshtam Yelena |
| author_sort | Mandelshtam Yelena |
| collection | DOAJ |
| description | In this paper we study graphs defined by pattern-avoiding words. Word-representable graphs have been studied extensively following their introduction in 2004 and are the subject of a book published by Kitaev and Lozin in 2015. Recently there has been interest in studying graphs represented by pattern-avoiding words. In particular, in 2016, Gao, Kitaev, and Zhang investigated 132-representable graphs, that is, word-representable graphs that can be represented by a word which avoids the pattern 132. They proved that all 132-representable graphs are circle graphs and provided examples and properties of 132-representable graphs. They posed several questions, some of which we answer in this paper. |
| first_indexed | 2024-03-12T08:44:52Z |
| format | Article |
| id | doaj.art-6787eeeea85647eea449ac973e607da1 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T08:44:52Z |
| publishDate | 2019-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-6787eeeea85647eea449ac973e607da12023-09-02T16:29:57ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922019-05-0139237538910.7151/dmgt.2128dmgt.2128On Graphs Representable by Pattern-Avoiding WordsMandelshtam Yelena0Stanford University, Stanford, CA, USAIn this paper we study graphs defined by pattern-avoiding words. Word-representable graphs have been studied extensively following their introduction in 2004 and are the subject of a book published by Kitaev and Lozin in 2015. Recently there has been interest in studying graphs represented by pattern-avoiding words. In particular, in 2016, Gao, Kitaev, and Zhang investigated 132-representable graphs, that is, word-representable graphs that can be represented by a word which avoids the pattern 132. They proved that all 132-representable graphs are circle graphs and provided examples and properties of 132-representable graphs. They posed several questions, some of which we answer in this paper.https://doi.org/10.7151/dmgt.2128pattern-avoidanceword-representabilitycircle graphs05c99 |
| spellingShingle | Mandelshtam Yelena On Graphs Representable by Pattern-Avoiding Words Discussiones Mathematicae Graph Theory pattern-avoidance word-representability circle graphs 05c99 |
| title | On Graphs Representable by Pattern-Avoiding Words |
| title_full | On Graphs Representable by Pattern-Avoiding Words |
| title_fullStr | On Graphs Representable by Pattern-Avoiding Words |
| title_full_unstemmed | On Graphs Representable by Pattern-Avoiding Words |
| title_short | On Graphs Representable by Pattern-Avoiding Words |
| title_sort | on graphs representable by pattern avoiding words |
| topic | pattern-avoidance word-representability circle graphs 05c99 |
| url | https://doi.org/10.7151/dmgt.2128 |
| work_keys_str_mv | AT mandelshtamyelena ongraphsrepresentablebypatternavoidingwords |