Multidesigns for the graph pair formed by the 6-cycle and 3-prism

<p class="p1">Given two graphs <em>G</em> and <em>H</em>, a (<em>G</em>,<em>H</em>)-multidecomposition of <em>K<sub>n</sub></em> is a partition of the edges of <em>K<sub>n</sub></em> into...

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Bibliographic Details
Main Authors: Yizhe Gao, Dan Roberts
Format: Article
Language:English
Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2020-04-01
Series:Electronic Journal of Graph Theory and Applications
Subjects:
Online Access:https://www.ejgta.org/index.php/ejgta/article/view/896
Description
Summary:<p class="p1">Given two graphs <em>G</em> and <em>H</em>, a (<em>G</em>,<em>H</em>)-multidecomposition of <em>K<sub>n</sub></em> is a partition of the edges of <em>K<sub>n</sub></em> into copies of <em>G</em> and <em>H</em> such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of (C<sub>6</sub>,Ċ<sub>6</sub>)-multidecomposition of <em>K<sub>n</sub></em> where C<sub>6</sub> denotes a cycle of length 6 and C<sub>6</sub> denotes the complement of C<sub>6</sub>. We also characterize the cardinalities of leaves and paddings of maximum (C<sub>6</sub>,Ċ<sub>6</sub>)-multipackings and minimum (C<sub>6</sub>,Ċ<sub>6</sub>)-multicoverings, respectively.</p>
ISSN:2338-2287