| Title: | Retracts of products of chordal graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Chalopin, Jérémie (Author)
ID Chepoi, Victor (Author)
ID Kovše, Matjaž (Author)
ID Labourel, Arnaud (Author)
ID Vaxès, Yann (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/01134.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | We characterize the graphs ▫$G$▫ that are retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain ▫$K_{2;3}$▫, ▫$k$▫-wheels ▫$W_k$▫, and ▫$k$▫-wheels minus one spoke T$W_k^- ; (k ge 4)$T as induced subgraphs. We also show that these graphs ▫$G$▫ are exactly the cage-amalgamation graphs introduced by Brešar and Tepeh Horvat (2009); this solves the open question raised by these authors. Finally, we prove that replacing all products of cliques of $G$ by products of "solid" simplices, we obtain a polyhedral cell complex which, endowed with an intrinsic Euclidean metric, is a CAT(0) space. This generalizes similar results about median graphs as retracts of hypercubes (products of edges) and median graphs as 1-skeletons of CAT(0) cubical complexes. |
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| Keywords: | teorija grafov, graf, retrakt, zastražena amalgamacija, tetiven graf, kartezični produkt grafov, medianski graf, graph theory, graph, retract, gated amalgamation, chordal graph, Cartesian product of graphs, median graph |
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| Year of publishing: | 2010 |
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| Number of pages: | str. 1-20 |
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| Numbering: | Vol. 48, št. 1134 |
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| PID: | 20.500.12556/DKUM-51873  |
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| ISSN: | 2232-2094 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 15751513 |
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| NUK URN: | URN:SI:UM:DK:NGAKPCB0 |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1429 |
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| Downloads: | 114 |
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| Metadata: |    |
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| Categories: | Misc.
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