Note on strong product graph dimension

Jaroslav Nešetřil, Aleš Pultr
2022 The Art of Discrete and Applied Mathematics  
In this paper we define a new dimension of graphs based on the strong product. Strong product can be viewed as a categorical product in a modified category. Unlike in the standard case where the system of basic generators ("simplest objects") is very transparent but necessarily infinite, we have here a single generator. Using just a single generator would lead to increasing complexity value even for structurally very trivial objects just because of the size. Thus, for more satisfactory results,
more » ... it is advisable to use a transparent infinite system. Such one is proposed and several estimates for the resulting dimension are proved.
doi:10.26493/2590-9770.1523.2d7 fatcat:nfdfao5xrjahnha6afmnlhorla