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Tytuł:
Kernels by monochromatic paths and the color-class digraph
Autorzy:
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/743879.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel by monochromatic paths
the color-class digraph
Opis:
An m-colored digraph is a digraph whose arcs are colored with m colors. A directed path is monochromatic when its arcs are colored alike.
A set S ⊆ V(D) is a kernel by monochromatic paths whenever the two following conditions hold:
1. For any x,y ∈ S, x ≠ y, there is no monochromatic directed path between them.
2. For each z ∈ (V(D)-S) there exists a zS-monochromatic directed path.
In this paper it is introduced the concept of color-class digraph to prove that if D is an m-colored strongly connected finite digraph such that:
(i) Every closed directed walk has an even number of color changes,
(ii) Every directed walk starting and ending with the same color has an even number of color changes, then D has a kernel by monochromatic paths.
This result generalizes a classical result by Sands, Sauer and Woodrow which asserts that any 2-colored digraph has a kernel by monochromatic paths, in case that the digraph D be a strongly connected digraph.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 2; 273-281
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cycle-pancyclism in bipartite tournaments II
Autorzy:
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/744263.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bipartite tournament
pancyclism
Opis:
Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T, and k an even number. In this paper the following question is studied: What is the maximum intersection with γ of a directed cycle of length k contained in T[V(γ)]? It is proved that for an even k in the range (n+6)/2 ≤ k ≤ n-2, there exists a directed cycle $C_{h(k)}$ of length h(k), h(k) ∈ {k,k-2} with $|A(C_{h(k)}) ∩ A(γ)| ≥ h(k)-4$ and the result is best possible. In a previous paper a similar result for 4 ≤ k ≤ (n+4)/2 was proved.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 529-538
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some sufficient conditions on odd directed cycles of bounded length for the existence of a kernel
Autorzy:
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/744469.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel-perfect
critical kernel-imperfect
Opis:
A kernel N of a digraph D is an independent set of vertices of D such that for every w ∈ V(D)-N there exists an arc from w to N. If every induced subdigraph of D has a kernel, D is said to be a kernel-perfect digraph. In this paper I investigate some sufficient conditions for a digraph to have a kernel by asking for the existence of certain diagonals or symmetrical arcs in each odd directed cycle whose length is at most 2α(D)+1, where α(D) is the maximum cardinality of an independent vertex set of D. Previous results are generalized.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 2; 171-182
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cycle-pancyclism in bipartite tournaments I
Autorzy:
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/744498.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bipartite tournament
pancyclism
Opis:
Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T, and k an even number. In this paper, the following question is studied: What is the maximum intersection with γ of a directed cycle of length k? It is proved that for an even k in the range 4 ≤ k ≤ [(n+4)/2], there exists a directed cycle $C_{h(k)}$ of length h(k), h(k) ∈ {k,k-2} with $|A(C_{h(k)}) ∩ A(γ)| ≥ h(k)-3$ and the result is best possible.
In a forthcoming paper the case of directed cycles of length k, k even and k < [(n+4)/2] will be studied.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 2; 277-290
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
k-Kernels and some operations in digraphs
Autorzy:
Galeana-Sanchez, Hortensia
Pastrana, Laura
Powiązania:
https://bibliotekanauki.pl/articles/743109.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
k-kernel
k-subdivision digraph
k-middle digraph and k-total digraph
Opis:
Let D be a digraph. V(D) denotes the set of vertices of D; a set N ⊆ V(D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u,v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-directed path of length at most k-1. In this paper, we consider some operations on digraphs and prove the existence of k-kernels in digraphs formed by these operations from another digraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 1; 39-49
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Directed hypergraphs: a tool for researching digraphs and hypergraphs
Autorzy:
Galeana-Sánchez, Hortensia
Manrique, Martín
Powiązania:
https://bibliotekanauki.pl/articles/743191.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypergraph
strongly independent set
transversal set
kernel
Opis:
In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level of any edge they belong to. Some little adjustments are needed to avoid directed walks within a single edge of the underlying hypergraph, and to deal with isolated vertices.
The concepts of independent set, absorbent set, and transversal set are inherited directly from digraphs.
As a consequence of our results on this topic, we have found both a class of kernel-perfect digraphs with odd cycles and a class of hypergraphs which have a strongly independent transversal set.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 313-335
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings
Autorzy:
Galeana-Sánchez, Hortensia
Gómez, Ricardo
Powiązania:
https://bibliotekanauki.pl/articles/743799.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
state splitting
line digraph
kernel
Grundy function
duality
Opis:
Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 2; 359-371
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monochromatic kernel-perfectness of special classes of digraphs
Autorzy:
Galeana-Sánchez, Hortensia
Ramírez, Luis
Powiązania:
https://bibliotekanauki.pl/articles/743807.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel by monochromatic paths
composition
duplication
Opis:
In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results:
(1) If D is a digraph without monochromatic directed cycles, then D and each $α_v,v ∈ V(D)$ are monochromatic kernel-perfect digraphs if and only if the composition over D of $(α_v)_{v ∈ V(D)}$ is a monochromatic kernel-perfect digraph.
(2) D is a monochromatic kernel-perfect digraph if and only if for any B ⊆ V(D), the duplication of D over B, $D^B$, is a monochromatic kernel-perfect digraph.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 389-400
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A conjecture on cycle-pancyclism in tournaments
Autorzy:
Galeana-Sánchez, Hortensia
Rajsbaum, Sergio
Powiązania:
https://bibliotekanauki.pl/articles/744233.pdf
Data publikacji:
1998
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Tournaments
pancyclism
cycle-pancyclism
Opis:
Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T. In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Cₖ of length k in T we denote $I_γ (Cₖ) = |A(γ)∩A(Cₖ)|$, the number of arcs that γ and Cₖ have in common. Let $f(k,T,γ) = max{I_γ(Cₖ)|Cₖ ⊂ T}$ and f(n,k) = min{f(k,T,γ)|T is a hamiltonian tournament with n vertices, and γ a hamiltonian cycle of T}. In previous papers we gave a characterization of f(n,k). In particular, the characterization implies that f(n,k) ≥ k-4.
The purpose of this paper is to give some support to the following original conjecture: for any vertex v there exists a cycle of length k containing v with f(n,k) arcs in common with γ.
Źródło:
Discussiones Mathematicae Graph Theory; 1998, 18, 2; 243-251
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kernels and cycles subdivisions in arc-colored tournaments
Autorzy:
Delgado-Escalante, Pietra
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/743117.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel by monochromatic paths
tournament
Opis:
Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there is an xn-monochromatic directed path in D. In this paper we prove that if T is an arc-colored tournament which does not contain certain subdivisions of cycles then it possesses a kernel by monochromatic paths. These results generalize a well known sufficient condition for the existence of a kernel by monochromatic paths obtained by Shen Minggang in 1988 and another one obtained by Hahn et al. in 2004. Some open problems are proposed.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 1; 101-117
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect
Autorzy:
Galeana-Sánchez, Hortensia
García-Ruvalcaba, José
Powiązania:
https://bibliotekanauki.pl/articles/743429.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel-perfect digraph
m-coloured digraph
Opis:
A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel.
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows:
V( ζ(D)) = V(D), and
A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic path of colour i from the vertex u to the vertex v contained in D}.
We will denoted by T₃ and C₃, the transitive tournament of order 3 and the 3-directed-cycle respectively; both of whose arcs are coloured with three different colours.
Let G be a simple graph. By an m-orientation-coloration of G we mean an m-coloured digraph which is an asymmetric orientation of G.
By the class E we mean the set of all the simple graphs G that for any m-orientation-coloration D without C₃ or T₃, we have that ζ(D) is a KP-digraph.
In this paper we prove that if G is a hamiltonian graph of class E, then its complement has at most one nontrivial component, and this component is K₃ or a star.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 77-93
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kernels by Monochromatic Paths and Color-Perfect Digraphs
Autorzy:
Galeana-Śanchez, Hortensia
Sánchez-López, Rocío
Powiązania:
https://bibliotekanauki.pl/articles/31340961.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel perfect digraph
kernel by monochromatic paths
color-class digraph
quasi color-perfect digraph
color-perfect digraph
Opis:
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 monochromatic directed path between them (N is mp-independent) and (2) for each vertex u in V (D) \ N there exists v ∈ N such that there is a monochromatic directed path from u to v in D (N is mp-absorbent). If every arc in D has a different color, then a kernel by monochromatic paths is said to be a kernel. Two associated digraphs to an arc-colored digraph are the closure and the color-class digraph C(D). In this paper we will approach an mp-kernel via the closure of induced subdigraphs of D which have the property of having few colors in their arcs with respect to D. We will introduce the concept of color-perfect digraph and we are going to prove that if D is an arc-colored digraph such that D is a quasi color-perfect digraph and C(D) is not strong, then D has an mp-kernel. Previous interesting results are generalized, as for example Richardson′s Theorem.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 309-321
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments
Autorzy:
Galeana-Sanchez, Hortensia
Rojas-Monroy, Rocío
Powiązania:
https://bibliotekanauki.pl/articles/743320.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel by monochromatic paths
bipartite tournament
Opis:
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
(i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and
(ii) for every vertex x ∈ V(D)∖N there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
In this paper it is proved that if D is an m-coloured bipartite tournament such that: every directed cycle of length 4 is quasi-monochromatic, every directed cycle of length 6 is monochromatic, and D has no induced particular 6-element bipartite tournament T̃₆, then D has a kernel by monochromatic paths.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 2; 285-306
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On monochromatic paths and bicolored subdigraphs in arc-colored tournaments
Autorzy:
Delgado-Escalante, Pietra
Galeana-Sánchez, Hortensia
Powiązania:
https://bibliotekanauki.pl/articles/743637.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
kernel by monochromatic paths
tournament
Opis:
Consider an arc-colored digraph. A set of vertices N is a kernel by monochromatic paths if all pairs of distinct vertices of N have no monochromatic directed path between them and if for every vertex v not in N there exists n ∈ N such that there is a monochromatic directed path from v to n. In this paper we prove different sufficient conditions which imply that an arc-colored tournament has a kernel by monochromatic paths. Our conditions concerns to some subdigraphs of T and its quasimonochromatic and bicolor coloration. We also prove that our conditions are not mutually implied and that they are not implied by those known previously. Besides some open problems are proposed.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 4; 791-820
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A class of tight circulant tournaments
Autorzy:
Galeana-Sánchez, Hortensia
Neumann-Lara, Víctor
Powiązania:
https://bibliotekanauki.pl/articles/743727.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Circulant tournament
acyclic disconnection
vertex 3-colouring
3-chromatic triangle
tight tournament
Opis:
A tournament is said to be tight whenever every 3-colouring of its vertices using the 3 colours, leaves at least one cyclic triangle all whose vertices have different colours. In this paper, we extend the class of known tight circulant tournaments.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 109-128
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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