Results 21 to 30 of about 39,621 (255)
Graph Minors and Minimum Degree [PDF]
The Electronic Journal of Combinatorics, 2010 Let $\mathcal{D}_k$ be the class of graphs for which every minor has minimum degree at most $k$. Then $\mathcal{D}_k$ is closed under taking minors. By the Robertson-Seymour graph minor theorem, $\mathcal{D}_k$ is characterised by a finite family of minor-minimal forbidden graphs, which we denote by $\widehat{\mathcal{D}}_k$.
Gasper Fijavz, David R. Wood
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Tree-width of hypergraphs and surface duality [PDF]
, 2008 In Graph Minors III, Robertson and Seymour write: "It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal - indeed, we have convinced ourselves that they differ by at most one".
Mazoit, Frédéric
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Inverse Eigenvalue Problems for Two Special Acyclic Matrices
Mathematics, 2016 In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix
Debashish Sharma, Mausumi Sen
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Discrete Applied Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reinhard Diestel, Daniela Kühn
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The Scientific World Journal, 2014 An n×n matrix is called an N0-matrix if all its specified principal minors are nonpositive. In the context of partial matrices, a partial matrix is called a partial N0-matrix if all its specified principal minors are nonpositive.
Cristina Jordán, Juan R. Torregrosa
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Deciding first-order properties of nowhere dense graphs [PDF]
, 2014 Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes
Courcelle B. +4 more
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A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor [PDF]
, 2013 Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles}. A {\em partition oracle} is a procedure that, given access to the incidence lists representation of a bounded ...
Levi, Reut, Ron, Dana
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Unavoidable Parallel Minors of 4-Connected Graphs [PDF]
, 2008 A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a
Chun, Carolyn +3 more
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on the number of cliques and cycles in graphs [PDF]
Transactions on Combinatorics, 2013 We give a new recursive method to compute the number of cliques and cycles of a graph. This method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the ...
Mojgan Emami, Masoud Ariannejad
doaj
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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