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2014 | 34 | 1 | 137-150
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Tree-Like Partial Hamming Graphs

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and give a new proof of that result, which holds also for a bigger class of graphs, so called tree-like partial Hamming graphs. We investigate these graphs and show some results which imply previously-known results on tree-like partial cubes. For instance, we characterize tree-like partial Hamming graphs and prove that every tree-like partial Hamming graph G contains a Hamming graph that is invariant under every automorphism of G. The latter result is a direct consequence of the result about the dismantlability of the intersection graph of maximal Hamming graphs of a tree-like partial Hamming graph.
Wydawca
Rocznik
Tom
34
Numer
1
Strony
137-150
Opis fizyczny
Daty
wydano
2014-02-01
online
2014-02-14
Twórcy
Bibliografia
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  • [8] B. Brešar, W. Imrich and S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory 23 (2003) 227-240. doi:10.7151/dmgt.1199[Crossref]
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1723
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