Graphs on Surfaces

By Bojan Mohar, C. Thomassen. Johns Hopkins series in the mathematical sciences, 2001

1,378 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0f86bf557ad8eabd3d5cdcf9799e4a30c8de4ab8

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Citations in the corpus

The chromatic polynomial of fatgraphs and its categorification (2005, background): “nected component of Gwith its rotation by ˇ around the axis determined by its 2-connecting vertices. For example, : The following theorem relates two planar embeddings of the same graph (see [31], or [32]). Theorem 6.3. Let Gbe a connected graph and f;f0: G!S2 be two planar embeddings. Then f(G) and”
Logical complexity of graphs: a survey (2010, background): “, [56]), they have a unique, up to homeomorphism, embedding into the sphere.”
A Characterization of the Tutte Polynomial via Combinatorial Embeddings (2006, background): “nar embedding. In fact, combinatorial embeddings are closely related to the embeddings of graphs on surfaces. What we call surfaces are compact 2-dimensional orientable surfaces without boundary (see [17]). An embeddings of a graph G in a surface S is a drawing of G on S without intersecting edges s”
Geometric Graphs and Arrangements (2004, background): “The book [142] of Mohar and Thomassen contains a rich chapter on planar graphs with many references.”
Defective and Clustered Graph Colouring (2018, background): “See [177] for background on embeddings of graphs on surfaces.”
Scaling limits of random trees and planar maps (2011, methodology): “We will not enter into details, referring the reader to the book by Mohar and Thomassen [42] for a very complete exposition.”
Graph colorings, flows and perfect matchings (2017, methodology): “We refer the reader to the book by Mohar and Thomassen [142] for more details or any notion not defined here.”
An extremal problem for H -linked graphs (2005, unknown): “Since kg ′ ≤ g, it then follows (see [14]) that G embeds on Σ.”
Descriptive Complexity, Canonisation, and Definable Graph Structure Theory (2017, background): “For more background, I refer the reader to [24] (for planar graph s, [4] is also a good reference).”
Mixing graph colourings (2007, methodology): “A proof of this result may be found in [52]; specifically, see Theorem 8.”
Barrier coverage with wireless sensors (2005, unknown): “We refer the reader to [17] for more details on essential cycles and to [18] for more details on graphs embedded on surfaces.”