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Applied Mathematics and Computation, ISSN 0096-3003, 05/2018, Volume 325, pp. 246 - 251
A strong edge coloring of a graph is a proper edge coloring in which every color class is an induced matching. The strong chromatic index χs′(G) of a graph G... 
Odd graph | Strong chromatic index | Strong edge coloring | Planar graphs | Maximum average degree | MATHEMATICS, APPLIED | GIRTH
Journal Article
Ars Mathematica Contemporanea, ISSN 1855-3966, 2015, Volume 9, Issue 2, pp. 277 - 287
An edge coloring of a graph G is said to be an odd edge coloring if for each vertex v of G and each color c, the vertex v uses the color c an odd number of... 
Shannon triangle | Odd subgraph | Edge coloring | MATHEMATICS | MATHEMATICS, APPLIED | odd subgraph
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2013, Volume 313, Issue 20, pp. 2218 - 2222
A facial parity edge coloring of a 2-edge connected plane graph is an edge coloring where no two consecutive edges of a facial trail of any face receive the... 
Facial parity edge coloring | Plane graph | Odd graph | MATHEMATICS | Coloring | Planes | Facial | Mathematical analysis | Color | Graphs | Parity | Mathematics - Combinatorics
Journal Article
GRAPHS AND COMBINATORICS, ISSN 0911-0119, 07/2017, Volume 33, Issue 4, pp. 595 - 615
Let G be a graph whose each component has order at least 3. Let for some integer be an improper edge coloring of G (where adjacent edges may be assigned the... 
NP-hardness | MATHEMATICS | Odd/even color classes | DISTINGUISHING INDEX | Twin edge/vertex coloring | Modular chromatic index
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2016, Volume 36, Issue 1, pp. 117 - 125
An of is a -edge-coloring of having a property that for every vertex of degree ) = , ≥ , the maximum color, that is present at vertex , occurs at exactly... 
unique-maximum edge-coloring | weak-odd edge-coloring | maximum | weak-even edge-coloring | 05C35 | edge-coloring | 05C15 | Edge-coloring | Weak-odd edge-coloring | R-maximum k-edge-coloring | Weak-even edge-coloring | Unique-maximum edge-coloring | MATHEMATICS | r-maximum k-edge-coloring
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2018, Volume 87, Issue 4, pp. 460 - 474
An odd k‐edge‐coloring of a graph G is a (not necessarily proper) edge‐coloring with at most k colors such that each nonempty color class induces a graph in... 
Shannon triangle | odd graph | odd edge‐coloring | odd chromatic index | MATHEMATICS | SUBGRAPHS | odd edge-coloring
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 11/2019, Volume 92, Issue 3, pp. 304 - 321
An odd graph is a graph whose vertex degrees are all odd. As introduced by Pyber in 1991, an odd edge‐covering of graph G is a family of odd subgraphs that... 
odd edge‐coloring | odd subgraph | T‐join | odd edge‐covering | T-join | MATHEMATICS | odd edge-covering | odd edge-coloring
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2005, Volume 9, Issue 1, pp. 59 - 67
Journal Article
Ars Mathematica Contemporanea, ISSN 1855-3966, 2016, Volume 10, Issue 2, pp. 359 - 370
An edge-coloring of a graph G is said to be odd if for each vertex v of G and each color c, the vertex v either uses the color c an odd number of times or does... 
T-join | Subcubic graph | Odd chromatic index | Odd edge-covering | Odd edge-coloring | MATHEMATICS | MATHEMATICS, APPLIED | odd edge-coloring | odd chromatic index | odd edge-covering
Journal Article
Applied Mechanics and Materials, ISSN 1660-9336, 02/2014, Volume 513-517, Issue Applied Science, Materials Science and Information Technologies in Industry, pp. 1858 - 1862
Labelled models are used in researching areas of communication networks, cryptography, computer science, biology, information networks etc, and they are for... 
Labelling | Skolem-graceful | Odd-graceful | Edge coloring | Networks | Algorithms | Computer simulation | Mathematical models | Biology | Communication networks | Cryptography
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 12, pp. 4166 - 4170
We offer the following structural result: every triangle-free graph G of maximum degree 3 has 3 matchings which collectively cover at least ( 1 − 2 3 γ o ( G )... 
Edge-coloring | Odd girth | Petersen graph | Approximation algorithm | 3-edge-coloring | NP-COMPLETENESS | MATHEMATICS | EDGE | GRAPHS | Algorithms
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2018, Volume 341, Issue 12, pp. 3500 - 3512
In the last years, connection concepts such as rainbow connection and proper connection appeared in graph theory and received a lot of attention. In this... 
Odd connection | Trees | Edge colouring | Odd vertex-connection | Vertex colouring | 2-connected graphs | MATHEMATICS | PROPER CONNECTION | RAINBOW CONNECTION
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2016, Volume 339, Issue 10, pp. 2481 - 2489
For graphs G and H, the Ramsey number R(G,H) is the smallest positive integer N such that any red/blue edge coloring of KN contains either a red G or a blue H.... 
Regularity Lemma | Ramsey goodness | Stability Lemma | Fan and book | Odd cycle | MATHEMATICS | LEMMA | GRAPHS | Integers | Stability | Neural networks | Mathematical analysis | Graphs | Joining | Graph theory | Regularity
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2018, Volume 341, Issue 3, pp. 713 - 722
We study the class of simple graphs G∗ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the... 
Line graph | 2-connected | Kernel-perfect orientation | Chromatic index | Odd cycles | Edge list coloring | MATHEMATICS | LINE-GRAPHS | CHOOSABILITY
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2019, Volume 363, p. 124613
Let C2m+1={C3,C5,⋯,C2m+1} be the family of odd cycles of length at most 2m+1. The Class Ramsey number Rk(C2m+1) is defined as the smallest integer N such that... 
Class Ramsey number | Odd cycle | Ramsey number | MATHEMATICS, APPLIED
Journal Article
JOURNAL OF COMBINATORIAL THEORY SERIES B, ISSN 0095-8956, 05/2017, Volume 124, pp. 128 - 164
We present a necessary and sufficient condition for a graph of odd-girth 2k+1 to bound the class of K-4-minor-free graphs of odd-girth (at least) 2k+1, that... 
CIRCULAR CHROMATIC NUMBER | MATHEMATICS | DUALITIES | SERIES-PARALLEL GRAPHS | Series Parallel Graphs | PLANAR GRAPHS | Graph homomorphisms | LARGE ODD-GIRTH
Journal Article
Electronic Journal of Graph Theory and Applications, ISSN 2338-2287, 10/2015, Volume 3, Issue 2, pp. 133 - 145
We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose... 
distance-regular graph | odd graph | Grafs, Teoria de | spectrum | Matemàtiques i estadística | Graph theory | Àrees temàtiques de la UPC | distance-regular graph, odd graph, spectrum
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 05/2017, Volume 124, pp. 56 - 63
We show that for any positive integer r there exists an integer k and a k-colouring of the edges of K2k+1 with no monochromatic odd cycle of length less than... 
Ramsey numbers | Edge colourings | Odd cycles | MATHEMATICS
Journal Article
Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 12/2017, Volume 92
Conference Proceeding
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