Results 1 to 10 of about 193 (188)
Graph minors. XXI. Graphs with unique linkages
Journal of Combinatorial Theory Series B, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Seymour
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Explicit bounds for graph minors [PDF]
Journal of Combinatorial Theory Series B, 2018 24 pages, 0 ...
Bruce Richter, Tony Huynh
exaly +6 more sources
Minimum Degree and Graph Minors
Electronic Notes in Discrete Mathematics, 2008 Abstract A graph G is a minor minimal minimum degree graph (MMMD) if δ ( H ) δ ( G ) for every proper minor H of G. We (i) determine all complete multipartite MMMD graphs and show that (ii) every small k-regular graph is a MMMD graph. Intuitively it seems that MMMD graphs are highly connected.
David Wood
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Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian.
Miriam Farber, Yelena Mandelshtam
doaj +1 more source
The sandpile group of a thick cycle graph
Electronic Journal of Graph Theory and Applications, 2022 The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted.
Diane Christine Alar +4 more
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MINORS IN WEIGHTED GRAPHS [PDF]
Bulletin of the Australian Mathematical Society, 2008 AbstractWe define the notion of minor for weighted graphs. We prove that with this minor relation, the set of weighted graphs is directed. We also prove that, given any two weights on a connected graph with the same total weight, we can transform one into the other using a sequence of edge subdivisions and edge contractions.
Joiţa, Cezar, Joiţa, Daniela
openaire +1 more source
Minor-Universal Graph for Graphs on Surfaces
CoRR, 2023 We show that, for every n and every surface $Σ$, there is a graph U embeddable on $Σ$ with at most cn^2 vertices that contains as minor every graph embeddable on $Σ$ with n vertices. The constant c depends polynomially on the Euler genus of $Σ$. This generalizes a well-known result for planar graphs due to Robertson, Seymour, and Thomas [Quickly ...
Cyril Gavoille, Claire Hilaire
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Small minors in dense graphs [PDF]
European Journal of Combinatorics, 2012 A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph.
Samuel Fiorini +3 more
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Internally 4-Connected Graphs With No {Cube, V8}-Minor
Discussiones Mathematicae Graph Theory, 2021 A simple graph is a minor of another if the first is obtained from the second by deleting vertices, deleting edges, contracting edges, and deleting loops and parallel edges that are created when we contract edges.
Lewchalermvongs Chanun +1 more
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Implications of network topology on stability. [PDF]
PLoS ONE, 2015 In analogy to chemical reaction networks, I demonstrate the utility of expressing the governing equations of an arbitrary dynamical system (interaction network) as sums of real functions (generalized reactions) multiplied by real scalars (generalized ...
Ali Kinkhabwala
doaj +1 more source