2021/05/12 by Karen L. Collins, Collins, Karen L., Megan E. Heenehan +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C69 #msc:05C75 #msc:05C76
paper · pdf · doi:10.48550/arxiv.2105.05724
9 pages, 2 figures, submitted to Proceedings of the Southeastern Conference on Combinatorics, Graph Theory, and Computing
arxiv created 2021/05/12 · arxiv updated 2021/05/13
The immersion number of a graph G, denoted im(G), is the largest t such that G has a Kt-immersion. In this note we are interested in determining the immersion number of the m-Mycielskian of G, denoted μm(G). Given the immersion number of G we provide a lower bound for im(μm(G)). To do this we introduce the "distinct neighbor property" of immersions. We also include examples of classes of graphs where im(μm(G)) exceeds the lower bound. We conclude with a conjecture about im(μm(Kt)).