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Journal of the London Mathematical Society, ISSN 0024-6107, 02/2017, Volume 95, Issue 1, pp. 203 - 222
Given any integers s,t⩾2, we show that there exists some c=c(s,t)>0 such that any Ks,t‐free graph with average degree d contains a subdivision of a clique with... 
05C83 (secondary) | 05C35 (primary) | 05C38
Journal Article
Combinatorica, ISSN 0209-9683, 8/2018, Volume 38, Issue 4, pp. 827 - 845
We find the asymptotic value of the Ramsey number for a triple of long cycles, where the lengths of the cycles are large but may have different parity. 
Mathematics, general | Mathematics | 05C55 | Combinatorics | 05C38 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 2/2019, Volume 39, Issue 1, pp. 135 - 151
We provide sufficient conditions for the existence of long cycles in locally expanding graphs, and present applications of our conditions and techniques to... 
05D10 | Mathematics, general | Mathematics | 05C80 | Combinatorics | 05C35 | 05C57 | 05C38 | MATHEMATICS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 07/2018, Volume 88, Issue 3, pp. 385 - 401
A path cover of a graph is a set of disjoint paths so that every vertex in the graph is contained in one of the paths. The path cover number p(G) of graph G is... 
regular graphs | 05C70 | discharging | path cover | 05C38 | MATHEMATICS | DOMINATION
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 06/2016, Volume 82, Issue 2, pp. 121 - 153
Let H denote the tree with six vertices, two of which are adjacent and of degree 3. Let G be a graph and u1,u2,a1,a2,a3,a4 be distinct vertices of G. We... 
05C75 | independent paths | separation | 05C38 | 05C40
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 12/2013, Volume 62, Issue 4, pp. 779 - 792
Journal Article
Journal of Discrete Mathematical Sciences and Cryptography, ISSN 0972-0529, 08/2019, Volume 22, Issue 6, pp. 1077 - 1090
In this paper, the edge version of SDD and ISI index are introduced. Using this concept the explicit formulas for the edge version of SDD and ISI of rooted... 
46A63 | Line graph | Rooted product of graphs | 05C38 | Topological indices
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2019, Volume 47, Issue 5, pp. 1985 - 1996
An ideal I in a commutative Noetherian ring R has the strong persistence property if for all positive integers t. In this article, we focus on how some graph... 
Cycles | 05E40 | cover ideals | associated primes | wheel graphs | 13P25 | 05C25 | Helm graphs | 05C38
Journal Article
Combinatorica, ISSN 0209-9683, 8/2019, Volume 39, Issue 4, pp. 847 - 878
For any countably infinite graph G, Ramsey’s theorem guarantees an infinite monochromatic copy of G in any r-coloring of the edges of the countably infinite... 
Mathematics, general | Mathematics | 05C55 | Combinatorics | 05C38
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2019, Volume 39, Issue 1, pp. 271 - 284
Two vertices of the k-dimensional hypercube Q are antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is... 
hypercube | antipodal edge-coloring | 05C55 | monochromatic geodesic | 05C38 | Antipodal edge-coloring | Monochromatic geodesic | Hypercube | MATHEMATICS
Journal Article
Acta Universitatis Sapientiae, Informatica, ISSN 2066-7760, 08/2019, Volume 11, Issue 1, pp. 95 - 108
A vertex v of a given graph is said to be in a rainbow neighbourhood of G if every color class of G consists of at least one vertex from the closed... 
G.2.2 | 05C75 | rainbow neighbourhood | J-coloring | 05C85 | 05C38 | 05C15
Journal Article
Combinatorica, ISSN 0209-9683, 4/2019, Volume 39, Issue 2, pp. 239 - 263
In 2006, Barát and Thomassen conjectured that there is a function f such that, for every fixed tree T with t edges, every f(t)-edge-connected graph with its... 
05C40 | 05C07 | Mathematics, general | Mathematics | Combinatorics | 05C38 | 05C15 | MATHEMATICS | Computer Science | Discrete Mathematics
Journal Article
Combinatorica, ISSN 0209-9683, 9/2010, Volume 30, Issue 5, pp. 485 - 520
In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal pairs and an integer c.... 
Mathematics, general | Mathematics | Combinatorics | 68Q17 | 05C38 | MATHEMATICS | APPROXIMATION ALGORITHMS | HARDNESS | FLOW
Journal Article
European Journal of Applied Mathematics, ISSN 0956-7925, 03/2018, Volume 30, Issue 2, pp. 1 - 20
During the 125th European Study Group with Industry held in Limassol, Cyprus, 5-9 December 2016, one of the participating companies, Engino.net Ltd, posed a... 
05C90 | 68R10 | 05C38 | 94C15 | MATHEMATICS, APPLIED | Toys | Graph theory | Decomposition | Algorithms | Assembly | Computer Science - Discrete Mathematics
Journal Article
Combinatorica, ISSN 0209-9683, 4/2018, Volume 38, Issue 2, pp. 381 - 398
The connected tree-width of a graph is the minimum width of a tree-decomposition whose parts induce connected subgraphs. Long cycles are examples of graphs... 
05C12 | 05C83 | 05C40 | Mathematics, general | Mathematics | Combinatorics | 05C05 | 05C38 | MATHEMATICS
Journal Article
Combinatorica, ISSN 0209-9683, 8/2018, Volume 38, Issue 4, pp. 847 - 859
We prove that the cut space of any transitive graph G is a finitely generated Aut(G)-module if the same is true for its cycle space. This confirms a conjecture... 
Mathematics, general | Mathematics | Combinatorics | 05C25 | 05C63 | 05C38 | MATHEMATICS | TREES | CAYLEY-GRAPHS
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 7/2019, Volume 35, Issue 4, pp. 827 - 836
A hamiltonian walk in a digraph D is a closed spanning directed walk of D with minimum length. The length of a hamiltonian walk in D is called the hamiltonian... 
05C45 | Hamiltonian number | Hamiltonian spectrum | Mathematics | Engineering Design | Combinatorics | Orientation | 05C69 | 05C38 | MATHEMATICS | Integers | Graphs | Graph theory
Journal Article
Combinatorica, ISSN 0209-9683, 4/2014, Volume 34, Issue 2, pp. 207 - 252
In 1992, Xiaoya Zha conjectured that the line graph of a 3-connected non-planar graph contains a subdivision of K 5. In this paper we prove this conjecture.... 
05C76 | Mathematics, general | Mathematics | 05C83 | Combinatorics | 05C38
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 06/2016, Volume 82, Issue 2, pp. 154 - 164
We characterize the quartic (i.e., 4‐regular) multigraphs with the property that every edge lies in a triangle. The main result is that such graphs are either... 
Primary 05C75 | quartic graph | triangle | Secondary 05C38
Journal Article
Combinatorica, ISSN 0209-9683, 06/2017, Volume 37, Issue 3, pp. 481 - 494
More than twenty years ago ErdAs conjectured [4] that a triangle-free graph G of chromatic number kae k (0)(epsilon) contains cycles of at least k (2-epsilon)... 
05C35 | 05C38 | 05C15 | MATHEMATICS | LENGTHS
Journal Article
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