2017
DOI: 10.48550/arxiv.1708.07671
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Phase transitions in graphs on orientable surfaces

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

0
3
0

Year Published

2018
2018
2019
2019

Publication Types

Select...
2

Relationship

2
0

Authors

Journals

citations
Cited by 2 publications
(3 citation statements)
references
References 44 publications
0
3
0
Order By: Relevance
“…We start by stating two very useful ingredients (Lemma 2.10 and Lemma 2.11) concerning the number of appearances and triangulated appearances (the proofs of which will be given in Sections 7 and 8): The following result, recently given in [24] (see also [23]), will be of use to us as well (note that the brace notation used here is to be understood as meaning that both conditions must be satisfied simultaneously): Lemma 2.12. ([24], Theorem 5.2) Let g ≥ 0 be a constant.…”
Section: Key Lemmasmentioning
confidence: 99%
“…We start by stating two very useful ingredients (Lemma 2.10 and Lemma 2.11) concerning the number of appearances and triangulated appearances (the proofs of which will be given in Sections 7 and 8): The following result, recently given in [24] (see also [23]), will be of use to us as well (note that the brace notation used here is to be understood as meaning that both conditions must be satisfied simultaneously): Lemma 2.12. ([24], Theorem 5.2) Let g ≥ 0 be a constant.…”
Section: Key Lemmasmentioning
confidence: 99%
“…One of our motivations for this paper comes from recent work concerning random graphs on given surfaces. The typical properties of graphs with genus at most g have been studied in [8] and [18] for the case when g is a fixed constant, and questions have been posed on the likely behaviour when g is allowed to grow with n. Hence, in this section, we shall discuss the contiguity (see Definition 6.2) of such random graph models with G(n) and G(n, m).…”
Section: Contiguity With Random Graphs On Given Surfacesmentioning
confidence: 99%
“…colouring problems [29] and the manufacture of electrical circuits [12,24]). It is naturally intriguing to consider the genus of a random graph, and such matters are also related to random graphs on surfaces (see, for example, Question 8.13 of [18] and Section 9 of [8]). In addition, results on the genus of random bipartite graphs [16] were recently used to provide a polynomial-time approximation scheme for the genus of dense graphs [15].…”
Section: Introductionmentioning
confidence: 99%