9,987 research outputs found
Complexity issues on bounded restrictive H-coloring
AbstractWe consider a bounded version of the restrictive and the restrictive list H-coloring problem in which the number of pre-images of certain vertices of H is taken as parameter. We consider the decision and the counting versions, as well as, further variations of those problems. We provide complexity results identifying the cases when the problems are NP-complete or #P-complete or polynomial time solvable. We conclude stating some open problems
On the Four-Color-Map Theorem
Coloring planar Feynman diagrams in spinor quantum electrodynamics, is a non
trivial model soluble without computer. Four colors are necessary and
sufficient.Comment: 8 page
Strong Structural Controllability of Signed Networks
In this paper, we discuss the controllability of a family of linear
time-invariant (LTI) networks defined on a signed graph. In this direction, we
introduce the notion of positive and negative signed zero forcing sets for the
controllability analysis of positive and negative eigenvalues of system
matrices with the same sign pattern. A sufficient combinatorial condition that
ensures the strong structural controllability of signed networks is then
proposed. Moreover, an upper bound on the maximum multiplicity of positive and
negative eigenvalues associated with a signed graph is provided
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