Results 161 to 170 of about 193 (188)

Graph Minors

Springer Monographs in Mathematics
Zdenek Dvorak
exaly   +2 more sources

Minors in lifts of graphs

Random Structures & Algorithms, 2005
AbstractWe study here lifts and random lifts of graphs, as defined by Amit and Linial (Combinatorica 22 (2002), 1–18). We consider the Hadwiger number η and the Hajós number σ of ℓ‐lifts of Kn and analyze their extremal as well as their typical values (that is, for random lifts). When ℓ = 2, we show that ${n \over 2} \leq \eta \leq n$, and random lifts
Yotam Drier, Nathan Linial
openaire   +2 more sources

A Note on Oct1+-Minor-Free Graphs and Oct2+-Minor-Free Graphs

Journal of Interconnection Networks, 2022
Let [Formula: see text] and [Formula: see text] be the planar and non-planar graphs, respectively, obtained from the Octahedron by 3-splitting a vertex. For [Formula: see text], we prove that if a 4-connected graph is [Formula: see text]-minor-free, then it is [Formula: see text], [Formula: see text] [Formula: see text] or it is obtained from [Formula:
Wenyan Jia, Shuai Kou, Weihua Yang, Chengfu Qin   +3 more
openaire   +1 more source

Excluding Minors in Cubic Graphs

Combinatorics, Probability and Computing, 1996
Let P10\e be the graph obtained by deleting an edge from the Petersen graph. We give a decomposition theorem for cubic graphs with no minor isomorphic to P10\e. The decomposition is used to show that graphs in this class are 3-edge-colourable. We also consider an application to a conjecture due to Grötzsch which states that a planar graph is 3-edge ...
Kyriakos Kilakos, F. Bruce Shepherd
openaire   +2 more sources

Vertex-minors of graphs: A survey

Discrete Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Donggyu Kim, Sang-il Oum
openaire   +1 more source

Towards the Graph Minor Theorems for Directed Graphs

2015
Two key results of Robertson and Seymour's graph minor theory are:1.a structure theorem stating that all graphs excluding some fixed graph as a minor have a tree decomposition into pieces that are almost embeddable in a fixed surface.2.the k-disjoint paths problem is tractable when $$k$$ is a fixed constant: given a graph $$G$$ and $$k$$ pairs $$s_1 ...
Kawarabayashi, Ken-Ichi, Kreutzer, Stephan   +1 more
openaire   +1 more source

Minors in graphs of large girth

Random Structures & Algorithms, 2003
AbstractWe show that for every odd integer g ≥ 5 there exists a constant c such that every graph of minimum degree r and girth at least g contains a minor of minimum degree at least cr(g+1)/4. This is best possible up to the value of the constant c for g = 5, 7, and 11.
Daniela Kühn, Deryk Osthus
openaire   +2 more sources

Compact topological minors in graphs

Journal of Graph Theory, 2010
Summary: Let \(\varepsilon \) be a real number such that \(0 < \varepsilon < \frac{1}{2}\) and \(t\) a positive integer. Let \(n\) be a sufficiently large positive integer as a function of \(t\) and \(\varepsilon \). We show that every \(n\)-vertex graph with at least \(n^{1+\varepsilon }\) edges contains a subdivision of \(K_{t}\) in which each edge ...
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On fixing edges in graph minors

Graphs and Combinatorics, 1996
A characterization of graphs with certain minor-type property is given.
openaire   +1 more source

Complete minors in pseudorandom graphs

Random Structures and Algorithms, 2000
The author's stated purpose is ``to show that many well-known pseudorandom graphs \dots{} actually have very large complete minors.'' This is demonstrated for two families of graphs. For a graph \(G\), the Hadwiger number \(h(G)\) is the largest \(t\) such that \(G\) admits the complete graph \(K_t\) as a minor. The vertex set of the Paley graph \(P_q\)
openaire   +2 more sources