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Combinatorica (Budapest. 1981), ISSN 1439-6912, 2018, Volume 38, Issue 2, pp. 305 - 339
We introduce a class of infinite graphic matroids that contains all the motivating examples and satisfies an extension of Tutte’s excluded minors... 
Mathematics, general | 05B35 | Mathematics | Combinatorics | 05C63 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 6/2016, Volume 36, Issue 3, pp. 249 - 264
Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete.... 
03C15 | Mathematics, general | Mathematics | Combinatorics | 05C60 | 05C63 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 4/2015, Volume 35, Issue 2, pp. 215 - 233
We say that a graph G is (ℵ0,κ)-chromatic if Chr(G) = κ, while Chr(G′) ≤ ℵ0 for any subgraph G′ of G of size < |G|.The main result of this paper reads as... 
03E35 | Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C15 | MATHEMATICS
Journal Article
Nagoya Mathematical Journal, ISSN 0027-7630, 09/2012, Volume 207, pp. 95 - 138
In this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space of p -Dirichlet finite functions on... 
53C23 | 05C63 | 31C20
Journal Article
Combinatorica, ISSN 0209-9683, 4/2015, Volume 35, Issue 2, pp. 153 - 180
As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory... 
Mathematics, general | 05B35 | Mathematics | 05B40 | Combinatorics | 05C63 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 6/2019, Volume 39, Issue 3, pp. 545 - 596
We show that every connected graph has a spanning tree that displays all its topological ends. This proves a 1964 conjecture of Halin in corrected form, and... 
Mathematics, general | 05B35 | Mathematics | Combinatorics | 05C63 | MATHEMATICS | FINITE | CONNECTIVITY | INFINITE CYCLES
Journal Article
Combinatorica, ISSN 0209-9683, 2/2019, Volume 39, Issue 1, pp. 165 - 214
We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness... 
03E35 | Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C15 | MATHEMATICS | CONJECTURE
Journal Article
Combinatorica, ISSN 0209-9683, 6/2016, Volume 36, Issue 3, pp. 313 - 332
We construct spanning trees in locally finite hyperbolic graphs that represent their hyperbolic compactification in a good way: so that the tree has at least... 
Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C05 | 20F67 | MATHEMATICS | EMBEDDINGS | DIMENSION | SPACES
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 12/2015, Volume 80, Issue 4, pp. 313 - 322
Given an edge coloring of a graph with a set of m colors, we say that the graph is exactly m‐colored if each of the colors is used. In 1999, Stacey and Weidl,... 
05C65 | Secondary 05C63 | subjclassPrimary 05D10 | MATHEMATICS | THEOREM | COMPLETE SUBGRAPHS
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 3/2019, Volume 215, Issue 3, pp. 819 - 862
We extend the notion of canonical measures to all (possibly non-compact) metric graphs. This will allow us to introduce a notion of “hyperbolic measures” on... 
20F65 | 57M60 | 05C12 | 05C63 | Mathematics, general | 14H30 | Mathematics | 14T05 | MATHEMATICS | Graphs | Theorems | Riemann surfaces | Constraining
Journal Article
Discrete and Computational Geometry, ISSN 0179-5376, 07/2017, Volume 58, Issue 1, pp. 67 - 79
The aim of this paper is to clarify the relationship between Gromo-vhyperbolicity and amenability for planar maps. 
Non-amenable graph | Planar graph | Coarse geometry | Hyperbolic graph | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | Graph theory | Hyperbolic coordinates | 05C63 (Secondary) | 05C10 (Primary)
Journal Article
Mathematische Annalen, ISSN 0025-5831, 8/2017, Volume 368, Issue 3, pp. 1017 - 1058
We prove the existence of Veech groups having a critical exponent strictly greater than any elementary Fuchsian group (i.e. $${>}\frac{1}{2}$$ > 1 2 ) but... 
20F65 | Mathematics, general | Mathematics | 30F30 | 05C63 | MATHEMATICS | GENUS-2 | SERIES | TEICHMULLER-CURVES | SURFACES
Journal Article
Combinatorica, ISSN 0209-9683, 10/2017, Volume 37, Issue 5, pp. 1027 - 1037
We give an elementary proof of the theorem of Nash-Williams that a graph has an edge-decomposition into cycles if and only if it does not contain an odd cut.... 
Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C38 | 05C40 | MATHEMATICS | INFINITE-GRAPHS | Computer science
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 03/2019, Volume 292, Issue 3, pp. 524 - 539
A graph is one‐ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has... 
infinite graph | 05C63 | 05C40 | graph automorphism | tree decomposition | 20B27 | 05C05 | MATHEMATICS | WEGE | CONNECTIVITY | INFINITE
Journal Article
Combinatorica, ISSN 0209-9683, 8/2017, Volume 37, Issue 4, pp. 785 - 793
Erdős and Hajnal conjectured in 1966 that every graph of uncountable chromatic number contains a subgraph of infinite connectivity. We prove that every graph... 
Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C40 | 05C15 | MATHEMATICS
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 630 - 648
Two graphs G and H are hypomorphic if there exists a bijection φ:V(G)→V(H) such that G−v≅H−φ(v) for each v∈V(G). A graph G is reconstructible if H≅G for all H... 
05C63 (primary) | 05C60 | MATHEMATICS | WINGS | INFINITE-GRAPHS | CONNECTED GRAPHS | Mathematics - Combinatorics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 257 - 269
An L(2, 1)-labeling of a graph G = (V,E) is an assignment of nonnegative integers to V such that two adjacent vertices must receive numbers (labels) at least... 
05C78 | 1)-labeling | 05C63 | 05C15 | L(2, 1)-labeling | MATHEMATICS | LABELING GRAPHS | L(2,1)-labeling
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 12/2019, Volume 45, Issue 6, pp. 1839 - 1854
We show that the Hrushovski–Fraïssé limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $$ \alpha \in... 
Generic structures | Predimension | Pseudofinite structures | 05C63 | Ultraflat graphs | Mathematics, general | Mathematics | Hrushovski constructions | Strictly superstable | 03C99 | Lascar rank | MATHEMATICS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2019, Volume 292, Issue 9, pp. 2072 - 2091
We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph... 
critical vertex set | compactification | infinite graph | tangle | critical | 54D35 | 05C63 | end | MATHEMATICS | TOPOLOGICAL APPROACH | LOCALLY FINITE GRAPHS
Journal Article
Combinatorica, ISSN 0209-9683, 10/2017, Volume 37, Issue 5, pp. 1011 - 1026
Given a polynomial p(x 0,x 1,...,x k−1) over the reals ℝ, where each x i is an n-tuple of variables, we form its zero k-hypergraph H=(ℝ n , E), where the set E... 
Mathematics, general | Mathematics | Combinatorics | 05C63 | 05C15 | MATHEMATICS | DECOMPOSITION | THEOREM | PARTITIONING EUCLIDEAN-SPACE
Journal Article
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