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On kernels by monochromatic paths in the corona of digraphs
Open Mathematics, 2008 Abstract In this paper we derive necessary and sufficient conditions for the existence of kernels by monochromatic paths in the corona of digraphs. Using these results, we are able to prove the main result of this paper which provides necessary and sufficient conditions for the corona of digraphs to be monochromatic kernel-perfect ...
Włoch Iwona
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Kernels by Monochromatic Paths and Color-Perfect Digraphs
Discussiones Mathematicae Graph Theory, 2016 For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no
Galeana-Śanchez Hortensia +1 more
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H-kernels by walks in an () digraph
AKCE International Journal of Graphs and Combinatorics, 2019 Let be a digraph possibly with loops and a digraph without loops whose arcs are colored with the vertices of ( is said to be an -colored digraph). A directed walk in is said to be an -walk if and only if the consecutive colors encountered on form a ...
Hortensia Galeana-Sánchez +3 more
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(, )-kernels and Sands, Sauer and Woodrow’s theorem
AKCE International Journal of Graphs and Combinatorics, 2019 Let = ( (), ()) a digraph. Consider the set = { : is a non trivial finite directed path in } and let and two subsets of . A subset of () is said to be an (, )-kernel of if (1) for every subset {, } of there exists no -directed path such that ( is ...
Hortensia Galeana-Sánchez +2 more
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Kernels by monochromatic paths in
Discrete Applied Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Galeana-Sánchez, Hortensia +2 more
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H-Kernels in Unions of H-Colored Quasi-Transitive Digraphs
Discussiones Mathematicae Graph Theory, 2021 Let H be a digraph (possibly with loops) and D a digraph without loops whose arcs are colored with the vertices of H (D is said to be an H-colored digraph). For an arc (x, y) of D, its color is denoted by c(x, y). A directed path W = (v0, . .
Campero-Alonzo José Manuel +1 more
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Extensions of Richardson’s theorem for infinite digraphs and (𝒜, ℬ)-kernels
AKCE International Journal of Graphs and Combinatorics, 2020 Let D be a digraph and and two subsets of where = {P: P is a non trivial finite path in D}. A subset N of V(D) is said to be an ()-kernel of D if: (1) for every {u,v} N there exists no uv-path P such that P (N is -independent), (2) for every vertex x in ...
Hortensia Galeana-Sánchez +2 more
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Cycles and transitivity by monochromatic paths in arc-coloured digraphs
AKCE International Journal of Graphs and Combinatorics, 2015 A digraph D is an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a∈A(D), then colour(a) will denote the colour has been used on a.
Enrique Casas-Bautista +2 more
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Tournaments with kernels by monochromatic paths
Contributions to Discrete Mathematics, 2012 In this paper we prove the existence of kernels by monochromatic paths in m-coloured tournaments in which every cyclic tournament of order 3 is atmost 2-coloured in addition to other restrictions on the colouring ofcertain subdigraphs. We point out that in all previous results on kernelsby monochromatic paths in arc coloured tournaments, certain ...
Galeana-Sánchez, Hortensia +1 more
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Simultaneous Feedback Vertex Set: A Parameterized Perspective [PDF]
, 2015 Given a family of graphs $\mathcal{F}$, a graph $G$, and a positive integer $k$, the $\mathcal{F}$-Deletion problem asks whether we can delete at most $k$ vertices from $G$ to obtain a graph in $\mathcal{F}$.
Agrawal, Akanksha +3 more
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