WG 2016: Graph-Theoretic Concepts in Computer Science pp 74-84 | Cite as
Packing and Covering Immersion Models of Planar Subcubic Graphs
Conference paper
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Abstract
A graph H is an immersion of a graph G if H can be obtained by some subgraph G after lifting incident edges. We prove that there is a polynomial function \(f:{\mathbb {N}}\times {\mathbb {N}}\rightarrow {\mathbb {N}}\), such that if H is a connected planar subcubic graph on \(h>0\) edges, G is a graph, and k is a non-negative integer, then either G contains k vertex/edge-disjoint subgraphs, each containing H as an immersion, or G contains a set F of f(k, h) vertices/edges such that \(G\setminus F\) does not contain H as an immersion.
Keywords
Erdö–Pósa properties Graph immersions Packings and coverings in graphsReferences
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