On planarity of 3-jump graphs

Abstract

For a graph G of size m ≥ 1 and edge-induced subgraphs F and H of size k where 1 ≤ k ≤ m, the subgraph H is said to be obtained from the subgraph F by an edge jump if there exist four distinct vertices u, v, w and x such that uv ∈ E(F), wx ∈ E(G) - E(F), and H = F - uv + wx. The k-jump graph Jk(G) is that graph whose vertices correspond to the edge-induced subgraphs of size k of G where two vertices F and H of Jk(G) are adjacent if and only if H can be obtained from F by an edge jump. All connected graphs G for whose J3(G) is planar are determined. © 2016 Academic Publications, Ltd.