Results 31 to 40 of about 39,621 (255)
Graph minors and the crossing number of graphs
Electronic Notes in Discrete Mathematics, 2007 Abstract There are three general lower bound techniques for the crossing numbers of graphs, all of which can be traced back to Leighton's work on applications of crossing number in VLSI: the Crossing Lemma, the Bisection Method, and the Embedding Method. In this contribution, we sketch their adaptations to the minor crossing number.
Drago Bokal +3 more
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On cut polytopes and graph minors [PDF]
Discrete Optimization, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantinos Kaparis +2 more
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Tree-depth and vertex-minors [PDF]
, 2016 In a recent paper Kwon and Oum (2014), Kwon and Oum claim that every graph of bounded rank-width is a pivot-minor of a graph of bounded tree-width (while the converse has been known true already before).
Courcelle +17 more
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Graphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
, 2012 We prove that every graph of rank-width $k$ is a pivot-minor of a graph of tree-width at most $2k$. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank ...
Bandelt +10 more
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On the graph condition regarding the $F$-inverse cover problem [PDF]
, 2015 In their paper titled "On $F$-inverse covers of inverse monoids", Auinger and Szendrei have shown that every finite inverse monoid has an $F$-inverse cover if and only if each finite graph admits a locally finite group variety with a certain property. We
Szakács, Nóra
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Grid Minors of Graphs on the Torus
Journal of Combinatorial Theory, Series B, 1994 The face-width of a graph embedded on the torus is the smallest \(n\) such that there is a noncontractible cycle on the torus which intersects the graph in exactly \(n\) points. For example, the product of two \(n\)-cycles \(C_ n\times C_ n\) embeds on the torus with face-width \(n\); this embedding is called the toroidal \(n\)-grid. A graph \(H\) is a
de Graaf, M., Schrijver, A.
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Coloring graphs with forbidden minors
Journal of Combinatorial Theory, Series B, 2017 Hadwiger's conjecture from 1943 states that for every integer $t\ge1$, every graph either can be $t$-colored or has a subgraph that can be contracted to the complete graph on $t+1$ vertices. As pointed out by Paul Seymour in his recent survey on Hadwiger's conjecture, proving that graphs with no $K_7$ minor are $6$-colorable is the first case of ...
Martin Rolek, Zi-Xia Song
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Graphs with no $\bar P_7$-Minor [PDF]
The Electronic Journal of Combinatorics, 2016 Let $\bar P_7$ denote the complement of a path on seven vertices. We determine all 4-connected graphs that do not contain $\bar P_7$ as a minor.
Guoli Ding +2 more
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The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations
AlgorithmsTree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width
Frank Gurski, Robin Weishaupt
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Models of Klein Surface Obstruction Graphs
Кібернетика та комп'ютерні технологіїThe task of researching the structure of graphs of given connectivity, which are obstructions for a given surface of non-oriented kind, and building their models, from which obstruction graphs are formed by removing or compressing a set of edges, is ...
Volodymyr Petrenjuk, Dmytro Petreniuk
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