Editing Cyclomatic number (section)

===Almost-trees===
A graph with cyclomatic number <math>r</math> is also called an {{mvar|r}}''-almost-tree'', because only {{mvar|r}} edges need to be removed from the graph to make it into a tree or forest.  A 1-almost-tree is a  ''near-tree'', and a connected near-tree is a [[pseudoforest|pseudotree]], a cycle with a (possibly trivial) tree rooted at each vertex.<ref name=CMC349>{{citation | last=Brualdi | first=Richard A. | title=Combinatorial Matrix Classes | series=Encyclopedia of Mathematics and Its Applications | volume=108 | location=Cambridge | publisher=[[Cambridge University Press]] | year=2006 | isbn=0-521-86565-4 | zbl=1106.05001 | page=[https://archive.org/details/combinatorialmat0000brua/page/349 349] | url=https://archive.org/details/combinatorialmat0000brua/page/349 }}</ref>

Several authors have studied the [[parameterized complexity]] of graph algorithms on {{mvar|r}}-near-trees, parameterized by <math>r</math>.<ref>{{citation
 | last1 = Coppersmith | first1 = Don | author1-link = Don Coppersmith
 | last2 = Vishkin | first2 = Uzi | author2-link = Uzi Vishkin
 | doi = 10.1016/0166-218X(85)90057-5 | zbl=0573.68017
 | issue = 1
 | journal = Discrete Applied Mathematics
 | pages = 27–45
 | title = Solving NP-hard problems in 'almost trees': Vertex cover
 | volume = 10
 | year = 1985| doi-access = free
 }}.</ref><ref>{{citation
 | last1 = Fiala | first1 = Jiří
 | last2 = Kloks | first2 = Ton
 | last3 = Kratochvíl | first3 = Jan
 | doi = 10.1016/S0166-218X(00)00387-5 | zbl=0982.05085
 | issue = 1
 | journal = Discrete Applied Mathematics
 | pages = 59–72
 | title = Fixed-parameter complexity of λ-labelings
 | volume = 113
 | year = 2001| doi-access = free
 }}.</ref>