Results 31 to 40 of about 193 (188)
On the choosability of -minor-free graphs
Combinatorics, Probability and Computing, 2023 AbstractGiven a graph $H$ , let us denote by $f_\chi (H)$ and $f_\ell (H)$ , respectively, the maximum chromatic number and the maximum list chromatic number of $H$ -minor-free graphs. Hadwiger’s famous colouring conjecture from 1943 states that $f_\chi (K_t)=t-1$ for every $t \ge 2$ .
Olivier Fischer, Raphael Steiner
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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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Clique Minors in Graphs and Their Complements
Journal of Combinatorial Theory, Series B, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bruce A. Reed, Robin Thomas 0001
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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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Contraction and Treewidth Lower Bounds
Journal of Graph Algorithms and Applications, 2006 Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree.
Hans Bodlaender +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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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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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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On graph contractions and induced minors [PDF]
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pim van 't Hof +4 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background Type 1 plasminogen deficiency (PLGD‐1) is an ultra‐rare autosomal recessive disorder caused by variants in the PLG gene and affects approximately 1.6 individuals per million. The condition is characterized by decreased plasminogen levels and impaired function, resulting in fibrin‐rich lesions on mucous membranes throughout the body.
Charles Nakar +7 more
wiley +1 more source