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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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
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 |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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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