Independent coverings and orthogonal colourings |
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| Authors: | Kyle MacKeigan |
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| Affiliation: | Department of Mathematics, Dalhousie University, Canada |
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| Abstract: | In this paper, two open conjectures are disproved. One conjecture regards independent coverings of sparse partite graphs, whereas the other conjecture regards orthogonal colourings of tree graphs. A relation between independent coverings and orthogonal colourings is established. This relation is applied to find independent coverings of some sparse partite graphs. Additionally, a degree condition providing the existence of an independent covering in the case where the graph has a square number of vertices is found. |
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| Keywords: | Orthogonal colouring Independent covering Tree graph Sparse partite graph Independent transversal |
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