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1
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Light Graphs In Planar Graphs Of Large Girth

100%
Hudák P., Maceková M., Madaras T., Široczki P.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 1
227-238
EN
A graph H is defined to be light in a graph family 𝒢 if there exist finite numbers φ(H, 𝒢) and w(H, 𝒢) such that each G ∈ 𝒢 which contains H as a subgraph, also contains its isomorphic copy K with ΔG(K) ≤ φ(H, 𝒢) and ∑x∈V(K) degG(x) ≤ w(H, 𝒢). In this paper, we investigate light graphs in families of plane graphs of minimum degree 2 with prescribed girth and no adjacent 2-vertices, specifying several necessary conditions for their lightness and providing sharp bounds on φ and w for light K1,3 and C10.
2
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Minimal regular graphs with given girths and crossing numbers

100%
Chia G., Gan C.
Discussiones Mathematicae Graph Theory
|
2004
|
tom 24
|
nr 2
223-237
EN
This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
3
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A note on total colorings of planar graphs without 4-cycles

100%
Wang P., Wu J.-L.
Discussiones Mathematicae Graph Theory
|
2004
|
tom 24
|
nr 1
125-135
EN
Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ {(7,4),(6,5),(5,7),(4,14)}.
4
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An ideal-based zero-divisor graph of direct products of commutative rings

88%
Atani S., Kohan M., Sarvandi Z.
Discussiones Mathematicae - General Algebra and Applications
|
2014
|
tom 34
|
nr 1
45-53
EN
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
5
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Maximizing Spectral Radii of Uniform Hypergraphs with Few Edges

88%
Fan Y.-Z., Tan Y.-Y., Peng X.-X., Liu A.-H.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 4
845-856
EN
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.
6
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Detour chromatic numbers

75%
Frick M., Bullock F.
Discussiones Mathematicae Graph Theory
|
2001
|
tom 21
|
nr 2
283-291
EN
The nth detour chromatic number, χₙ(G) of a graph G is the minimum number of colours required to colour the vertices of G such that no path with more than n vertices is monocoloured. The number of vertices in a longest path of G is denoted by τ( G). We conjecture that χₙ(G) ≤ ⎡(τ(G))/n⎤ for every graph G and every n ≥ 1 and we prove results that support the conjecture. We also present some sufficient conditions for a graph to have nth chromatic number at most 2.
7
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Some applications of pq-groups in graph theory

75%
Exoo G.
Discussiones Mathematicae Graph Theory
|
2004
|
tom 24
|
nr 1
109-114
EN
We describe some new applications of nonabelian pq-groups to construction problems in Graph Theory. The constructions include the smallest known trivalent graph of girth 17, the smallest known regular graphs of girth five for several degrees, along with four edge colorings of complete graphs that improve lower bounds on classical Ramsey numbers.
8
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L(2, 1)-Labelings of Some Families of Oriented Planar Graphs

63%
Sen S.
Discussiones Mathematicae Graph Theory
|
2014
|
tom 34
|
nr 1
31-48
EN
In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.
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