On one-sided interval edge colorings of biregular bipartite graphs
A proper edge \(t\)-coloring of a graph $G$ is a coloring of edges of\(G\) with colors \(1,2,\ldots,t\) such that all colors are used, and notwo adjacent edges receive the same color. The set of colors ofedges incident with a vertex \(x\) is called a spectrum of \(x\). Anynonempty subset of consecut...
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| Datum: | 2015 |
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Lugansk National Taras Shevchenko University
2015
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/46 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543036191801344 |
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| author | Kamalian, Rafayel Ruben |
| author_facet | Kamalian, Rafayel Ruben |
| author_sort | Kamalian, Rafayel Ruben |
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| collection | OJS |
| datestamp_date | 2015-09-28T11:22:08Z |
| description | A proper edge \(t\)-coloring of a graph $G$ is a coloring of edges of\(G\) with colors \(1,2,\ldots,t\) such that all colors are used, and notwo adjacent edges receive the same color. The set of colors ofedges incident with a vertex \(x\) is called a spectrum of \(x\). Anynonempty subset of consecutive integers is called an interval. Aproper edge \(t\)-coloring of a graph \(G\) is interval in the vertex$x$ if the spectrum of \(x\) is an interval. A proper edge\(t\)-coloring \(\varphi\) of a graph \(G\) is interval on a subset \(R_0\)of vertices of \(G\), if for any \(x\in R_0\), \(\varphi\) is interval in\(x\). A subset \(R\) of vertices of \(G\) has an \(i\)-property if there isa proper edge \(t\)-coloring of \(G\) which is interval on \(R\). If \(G\)is a graph, and a subset \(R\) of its vertices has an \(i\)-property,then the minimum value of \(t\) for which there is a proper edge\(t\)-coloring of \(G\) interval on \(R\) is denoted by \(w_R(G)\). We estimate the value of this parameter for biregular bipartite graphs in the case when \(R\) is one of the sides of a bipartition of the graph. |
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| format | Article |
| id | admjournalluguniveduua-article-46 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:21Z |
| publishDate | 2015 |
| publisher | Lugansk National Taras Shevchenko University |
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| spelling | admjournalluguniveduua-article-462015-09-28T11:22:08Z On one-sided interval edge colorings of biregular bipartite graphs Kamalian, Rafayel Ruben proper edge coloring, interval edge coloring, interval 05C15, 05C50, 05C85 A proper edge \(t\)-coloring of a graph $G$ is a coloring of edges of\(G\) with colors \(1,2,\ldots,t\) such that all colors are used, and notwo adjacent edges receive the same color. The set of colors ofedges incident with a vertex \(x\) is called a spectrum of \(x\). Anynonempty subset of consecutive integers is called an interval. Aproper edge \(t\)-coloring of a graph \(G\) is interval in the vertex$x$ if the spectrum of \(x\) is an interval. A proper edge\(t\)-coloring \(\varphi\) of a graph \(G\) is interval on a subset \(R_0\)of vertices of \(G\), if for any \(x\in R_0\), \(\varphi\) is interval in\(x\). A subset \(R\) of vertices of \(G\) has an \(i\)-property if there isa proper edge \(t\)-coloring of \(G\) which is interval on \(R\). If \(G\)is a graph, and a subset \(R\) of its vertices has an \(i\)-property,then the minimum value of \(t\) for which there is a proper edge\(t\)-coloring of \(G\) interval on \(R\) is denoted by \(w_R(G)\). We estimate the value of this parameter for biregular bipartite graphs in the case when \(R\) is one of the sides of a bipartition of the graph. Lugansk National Taras Shevchenko University 2015-09-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/46 Algebra and Discrete Mathematics; Vol 19, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/46/13 Copyright (c) 2015 Algebra and Discrete Mathematics |
| spellingShingle | proper edge coloring interval edge coloring interval 05C15 05C50 05C85 Kamalian, Rafayel Ruben On one-sided interval edge colorings of biregular bipartite graphs |
| title | On one-sided interval edge colorings of biregular bipartite graphs |
| title_full | On one-sided interval edge colorings of biregular bipartite graphs |
| title_fullStr | On one-sided interval edge colorings of biregular bipartite graphs |
| title_full_unstemmed | On one-sided interval edge colorings of biregular bipartite graphs |
| title_short | On one-sided interval edge colorings of biregular bipartite graphs |
| title_sort | on one-sided interval edge colorings of biregular bipartite graphs |
| topic | proper edge coloring interval edge coloring interval 05C15 05C50 05C85 |
| topic_facet | proper edge coloring interval edge coloring interval 05C15 05C50 05C85 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/46 |
| work_keys_str_mv | AT kamalianrafayelruben ononesidedintervaledgecoloringsofbiregularbipartitegraphs |