5 research outputs found
Minor-Obstructions for Apex-Pseudoforests
A graph is called a pseudoforest if none of its connected components contains
more than one cycle. A graph is an apex-pseudoforest if it can become a
pseudoforest by removing one of its vertices. We identify 33 graphs that form
the minor-obstruction set of the class of apex-pseudoforests, i.e., the set of
all minor-minimal graphs that are not apex-pseudoforests
Branchwidth is (1,g)-self-dual
A graph parameter is self-dual in some class of graphs embeddable in some
surface if its value does not change in the dual graph by more than a constant
factor. We prove that the branchwidth of connected hypergraphs without bridges
and loops that are embeddable in some surface of Euler genus at most g is an
(1,g)-self-dual parameter. This is the first proof that branchwidth is an
additively self-dual width parameter.Comment: 10 page
Minor obstructions for apex-pseudoforests
International audienceA graph is called a pseudoforest if none of its connected components contains more than one cycle. A graph is an apex-pseudoforest if it can become a pseudoforest by removing one of its vertices. We identify 33 graphs that form the minor obstruction set of the class of apex-pseudoforests, i.e., the set of all minor-minimal graphs that are not apex-pseudoforests
Minor obstructions for apex-pseudoforests
A graph is called a pseudoforest if none of its connected components
contains more than one cycle. A graph is an apex-pseudoforest if it can
become a pseudoforest by removing one of its vertices. We identify 33
graphs that form the minor obstruction set of the class of
apex-pseudoforests, i.e., the set of all minor-minimal graphs that are
not apex-pseudoforests. (C) 2021 Elsevier B.V. All rights reserved