Canonical Decompositions of 3-Connected Graphs
Copyright policy )Canonical Decompositions of 3-Connected Graphs
We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened K3,m’s. Our construction is explicit, canonical, and has the following applications: we obtain a new theorem characterising all finite Cayley graphs as either essentially 4-connected, cycles, or complete graphs on at most four vertices, and we provide an automatic proof of Tutte’s wheel theorem.
- University of Birmingham United Kingdom
FOS: Computer and information sciences, Connectivity, decomposition, Discrete Mathematics (cs.DM), Discrete Mathematics, Graph minors, 4-connected, 3-connected, Group actions on combinatorial structures, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), 3-separation, Combinatorics, FOS: Mathematics, canonical, wheel, Structural characterization of families of graphs, Combinatorics (math.CO), tri-separation, 05C40 (Primary), 05C75, 05C83, 05E18 (Secondary)
FOS: Computer and information sciences, Connectivity, decomposition, Discrete Mathematics (cs.DM), Discrete Mathematics, Graph minors, 4-connected, 3-connected, Group actions on combinatorial structures, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), 3-separation, Combinatorics, FOS: Mathematics, canonical, wheel, Structural characterization of families of graphs, Combinatorics (math.CO), tri-separation, 05C40 (Primary), 05C75, 05C83, 05E18 (Secondary)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!