Partitioning into Two Graphs with Only Small Components
نویسندگان
چکیده
The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree three has a vertex partition into two graphs, each of which has components on at most two vertices, and an edge partition into two graphs, each of which has components on at most eight vertices. It is not known whether similar results are true for maximum degree four and ve, but we show that a similar result is false for maximum degree six or higher, even for planar graphs.
منابع مشابه
Partitioning into graphs with only small components
The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree four has a vertex partition into two graphs, each of which has components on at most 57 vertices. Some generalizatio...
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