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» Pruning 2-Connected Graphs
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ENDM
2002
97views more  ENDM 2002»
13 years 5 months ago
Traceability in Small Claw-Free Graphs
We prove that a claw-free, 2-connected graph with fewer than 18 vertices is traceable, and we determine all non-traceable, claw-free, 2-connected graphs with exactly 18 vertices an...
John M. Harris, Michael J. Mossinghoff
LMCS
2006
119views more  LMCS 2006»
13 years 5 months ago
The monadic second-order logic of graphs XVI : Canonical graph decompositions
This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more ge...
Bruno Courcelle
ENDM
2006
75views more  ENDM 2006»
13 years 5 months ago
The structure and unlabelled enumeration of toroidal graphs with no K3, 3's
We characterize the toroidal graphs with no K3,3-subdivisions as canonical compositions in which 2-pole planar networks are substituted for the edges of non-planar cores. This str...
Andrei Gagarin, Gilbert Labelle, Pierre Leroux
DAM
2002
76views more  DAM 2002»
13 years 5 months ago
Block duplicate graphs and a hierarchy of chordal graphs
A block graph is a graph whose blocks are cliques. A block duplicate (BD) graph is a graph obtained by adding true twins (i.e., adjacent vertices with the same closed neighborhood...
Martin Charles Golumbic, Uri N. Peled
GC
2010
Springer
13 years 4 months ago
Enumerative Properties of Rooted Circuit Maps
In 1966 Barnette introduced a set of graphs, called circuit graphs, which are obtained from 3-connected planar graphs by deleting a vertex. Circuit graphs and 3-connected planar g...
Zhicheng Gao, Han Ren