Orthogonal Colourings of Tensor Graphs
Kyle MacKeigan

TL;DR
This paper investigates perfect k-orthogonal colourings of tensor graphs, reformulates the problem as a tensor subgraph problem, and establishes conditions and bounds for such colourings.
Contribution
It introduces a new tensor subgraph formulation for perfect orthogonal colourings and provides bounds and conditions for tensor graphs to have these colourings.
Findings
Reformulation of the 2-orthogonal colouring problem as a tensor subgraph problem
Establishment that tensor graphs inherit perfect k-orthogonal colourings from component graphs
Provision of new conditions for tensor graphs to admit perfect k-orthogonal colourings
Abstract
In this paper, perfect k-orthogonal colourings of tensor graphs are studied. First, the problem of determining if a given graph has a perfect 2-orthogonal colouring is reformulated as a tensor subgraph problem. Then, it is shown that if two graphs have a perfect -orthogonal colouring, then so does their tensor graph. This provides an upper bound on the -orthogonal chromatic number for general tensor graphs. Lastly, two other conditions for a tensor graph to have a perfect -orthogonal colouring are given.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Graph Labeling and Dimension Problems
