| Title: | On acyclic colorings of direct products |
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| Authors: | ID Špacapan, Simon (Author)
ID Tepeh, Aleksandra (Author) |
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| Files: |  Discussiones_Mathematicae_Graph_Theory_2008_Spacapan,_Tepeh_On_acyclic_colorings_of_direct_products.pdf (142,13 KB)
MD5: D9B4EBB189ABF137C6F5A73BF3A66322
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1363
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FS - Faculty of Mechanical Engineering
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| Abstract: | A coloring of a graph ▫$G$▫ is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees ▫$T_1$▫ and ▫$T_2$▫ equals ▫$\min\{ \Delta(T_1) + 1, \Delta(T_2) + 1\}$▫. We also prove that the acyclic chromatic number of direct product of two complete graphs ▫$K_m$▫ and ▫$K_n$▫ is ▫$mn-m-2$▫, where ▫$m \ge n \ge 4$▫. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised. |
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| Keywords: | mathematics, graph theory, coloring, acyclic coloring, distance-two coloring, direct product |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 323-333 |
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| Numbering: | Letn. 28, št. 2 |
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| PID: | 20.500.12556/DKUM-65349  |
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| ISSN: | 1234-3099 |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| COBISS.SI-ID: | 14893401 |
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| NUK URN: | URN:SI:UM:DK:8LGTYPFJ |
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| Publication date in DKUM: | 31.03.2017 |
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| Views: | 1084 |
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| Downloads: | 160 |
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| Metadata: |    |
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| Categories: | Misc.
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