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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Equivalent classes for K₃-gluings of wheels

100%
Bielak H.
Discussiones Mathematicae Graph Theory
|
1998
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tom 18
|
nr 1
73-84
EN
In this paper, the chromaticity of K₃-gluings of two wheels is studied. For each even integer n ≥ 6 and each odd integer 3 ≤ q ≤ [n/2] all K₃-gluings of wheels $W_{q+2}$ and $W_{n-q+2}$ create an χ-equivalent class.
2
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Chromatic polynomials of hypergraphs

100%
Borowiecki M., Łazuka E.
Discussiones Mathematicae Graph Theory
|
2000
|
tom 20
|
nr 2
293-301
EN
In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hypergraphs are chromatically unique. Moreover we give some equalities for the chromatic polynomials of hypergraphs generalizing known results for graphs and hypergraphs of Read and Dohmen.
3
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Hypergraphs with Pendant Paths are not Chromatically Unique

100%
Tomescu I.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 1
23-29
EN
In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.
4
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The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six

100%
Bielak H.
Discussiones Mathematicae Graph Theory
|
1998
|
tom 18
|
nr 1
99-111
EN
In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.
5
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On chromaticity of graphs

100%
Łazuka E.
Discussiones Mathematicae Graph Theory
|
1995
|
tom 15
|
nr 1
19-31
EN
In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.
6
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Chromatic Polynomials of Mixed Hypercycles

100%
Allagan J. A., Slutzky D.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 3
547-558
EN
We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any of its edges are colored with the same color (monochromatic) or when they are all colored with distinct colors (rainbow). In this paper, we determined explicit formulae for the chromatic polynomials of C-hypercycles and B-hypercycles
7
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An inductive proof of Whitney's Broken Circuit Theorem

100%
Dohmen K.
Discussiones Mathematicae Graph Theory
|
2011
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tom 31
|
nr 3
509-515
EN
We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.
8
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A Note on a Broken-Cycle Theorem for Hypergraphs

88%
Trinks M.
Discussiones Mathematicae Graph Theory
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2014
|
tom 34
|
nr 3
641-646
EN
Whitney’s Broken-cycle Theorem states the chromatic polynomial of a graph as a sum over special edge subsets. We give a definition of cycles in hypergraphs that preserves the statement of the theorem there
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