On the 4-girth-thickness of the line graph of the complete graph

zbMATH Open1464.05130arXiv1804.08723MaRDI QIDQ4989611

Christian Rubio-Montiel

Publication date: 25 May 2021

Abstract: The $g$-girth-thickness $heta(g,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least $g$ whose union is $G$. In this note, we give the $4$-girth-thickness $heta(4,L(K_n))$ of the line graph of the complete graph $L(K_n)$ when $n$ is even. We also give the minimum number of subgraphs of $L(K_n)$, which are of girth at least $4$ and embeddable on the projective plane, whose union is $L(K_n)$.

Full work available at URL: https://arxiv.org/abs/1804.08723

zbMATH Keywords

girth-thicknessplanar decomposition\(S\)-thicknessline graph token graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Graph operations (line graphs, products, etc.) (05C76)

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