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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Clique parts independent of remainders

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
2002
|
tom 22
|
nr 2
361
2
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Some maximum multigraphs and edge/vertex distance colourings

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
1995
|
tom 15
|
nr 1
89-106
EN
Shannon-Vizing-type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree Δ(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d-index and chromatic d-number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.
3
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Sums of Powered Characteristic Roots Count Distance-Independent Circular Sets

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
2013
|
tom 33
|
nr 1
217-229
EN
Significant values of a combinatorial count need not fit the recurrence for the count. Consequently, initial values of the count can much outnumber those for the recurrence. So is the case of the count, Gl(n), of distance-l independent sets on the cycle Cn, studied by Comtet for l ≥ 0 and n ≥ 1 [sic]. We prove that values of Gl(n) are nth power sums of the characteristic roots of the corresponding recurrence unless 2 ≤ n ≤ l. Lucas numbers L(n) are thus generalized since L(n) is the count in question if l = 1. Asymptotics of the count for 1 ≤ l ≤ 4 involves the golden ratio (if l = 1) and three of the four smallest Pisot numbers inclusive of the smallest of them, plastic number, if l = 4. It is shown that the transition from a recurrence to an OGF, or back, is best presented in terms of mutually reciprocal (shortly: coreciprocal) polynomials. Also the power sums of roots (i.e., moments) of a polynomial have the OGF expressed in terms of the co-reciprocal polynomial.
4
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Problems on fully irregular digraphs

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
1999
|
tom 19
|
nr 2
253-255
5
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On distance edge colourings of a cyclic multigraph

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
1999
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tom 19
|
nr 2
251-252
6
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'3in1' enhanced: three squared ways to '3in1' GRAPHS

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
2007
|
tom 27
|
nr 3
561-563
7
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A generalization of Sylvester's and Frobenius' problems on numerical semigroups

100%
Skupień Z.
Acta Arithmetica
|
1993
|
tom 65
|
nr 4
353-366
8
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Decompositions into two paths

100%
Skupień Z.
Discussiones Mathematicae Graph Theory
|
2005
|
tom 25
|
nr 3
325-329
EN
It is proved that a connected multigraph G which is the union of two edge-disjoint paths has another decomposition into two paths with the same set, U, of endvertices provided that the multigraph is neither a path nor cycle. Moreover, then the number of such decompositions is proved to be even unless the number is three, which occurs exactly if G is a tree homeomorphic with graph of either symbol + or ⊥. A multigraph on n vertices with exactly two traceable pairs is constructed for each n ≥ 3. The Thomason result on hamiltonian pairs is used and is proved to be sharp.
9
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Applied Graph Theory III. Euler and Hamilton graphs. Salesman problem.

64%
Sysło M. M., Skupień Z.
Mathematica Applicanda
|
1977
|
tom 5
|
nr 10
EN
A survey of some possible applications of graph theory to numerical analysis is given in part III. They are the following: (1) application of optimal trees to estimating the error in addition processes of positive floating-point numbers, (2) application of graphs to solving systems of linear equations, and (3) application of graphs in rearranging matrices to an easier-to-handle form.
10
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Decompositions of a complete multidigraph into almost arbitrary paths

64%
Meszka M., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2012
|
tom 32
|
nr 2
357-372
EN
For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n - 1 and different from n - 2, unless n = 5, λ = 1, and all lengths are to be n - 1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n - 2 can also be prescribed.
11
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Decompositions of nearly complete digraphs into t isomorphic parts

64%
Meszka M., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2009
|
tom 29
|
nr 3
563-572
EN
An arc decomposition of the complete digraph 𝒟 Kₙ into t isomorphic subdigraphs is generalized to the case where the numerical divisibility condition is not satisfied. Two sets of nearly tth parts are constructively proved to be nonempty. These are the floor tth class (𝒟 Kₙ-R)/t and the ceiling tth class (𝒟 Kₙ+S)/t, where R and S comprise (possibly copies of) arcs whose number is the smallest possible. The existence of cyclically 1-generated decompositions of 𝒟 Kₙ into cycles $^{→}C_{n-1}$ and into paths $^{→}Pₙ$ is characterized.
12
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Decompositions of multigraphs into parts with two edges

52%
Ivančo J., Meszka M., Skupień Z.
Discussiones Mathematicae Graph Theory
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2002
|
tom 22
|
nr 1
113-121
EN
Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.
13
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Counting Maximal Distance-Independent Sets in Grid Graphs

52%
Euler R., Oleksik P., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2013
|
tom 33
|
nr 3
531-557
EN
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
14
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A Sokoban-type game and arc deletion within irregular digraphs of all sizes

52%
Dziechcińska-Halamoda Z., Majcher Z., Majcher Z., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2007
|
tom 27
|
nr 3
611-622
EN
Digraphs in which ordered pairs of out- and in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the endpoints of these intervals) are found in [1,5]. In this paper we construct, with help of Sokoban-type game, n-vertex irregular oriented graphs (irregular digraphs) of all intermediate sizes.
15
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Extremum degree sets of irregular oriented graphs and pseudodigraphs

52%
Dziechcińska-Halamoda Z., Majcher Z., Michael J., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2006
|
tom 26
|
nr 2
317-333
EN
A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.
16
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On traceability and 2-factors in claw-free graphs

52%
Fronček D., Ryjáček Z., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2004
|
tom 24
|
nr 1
55-71
EN
If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σₖ > n + k² - 4k + 7 (where k is an arbitrary constant), then G has a 2-factor with at most k - 1 components. As a second main result, we present classes of graphs 𝓒₁,...,𝓒₈ such that every sufficiently large connected claw-free graph satisfying degree condition σ₆(k) > n + 19 (or, as a corollary, δ(G) > (n+19)/6) either belongs to $⋃ ⁸_{i=1} 𝓒_i$ or is traceable.
17
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On vertices and edges in maximum path-factors of a tree

45%
Skupień Z., Zygmunt W.
Fundamenta Mathematicae
|
1980
|
tom 109
|
nr 2
89-101
18
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Preface, Contents, Participants

38%
Skupień Z., Borowiecki M.
Banach Center Publications
|
1989
|
tom 25
|
nr 1
1-10
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