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Graphs and Combinatorics, ISSN 0911-0119, 1/2016, Volume 32, Issue 1, pp. 323 - 332
Given a tournament $$T$$ T , let $$h(T)$$ h ( T ) be the smallest integer $$k$$ k such that every arc-coloring of $$T$$ T with $$k$$ k or more colors produces... 
05C20 | Heterochromatic | Mathematics | Out-directed tree | Engineering Design | Combinatorics | Tournament | 05C35 | 05C15 | Coloring | Tournaments & championships | Graph theory | Integers | Texts | Graphs | Combinatorial analysis | Mathematics - Combinatorics
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 9/2019, Volume 35, Issue 5, pp. 989 - 999
We introduce the notion of a [z, r; g]-mixed cage. A [z, r; g]-mixed cage is a mixed graph G, z-regular by arcs, r-regular by edges, with girth g and minimum... 
Mixed cage | 05C20 | Mixed graph | Mathematics | Mixed Moore graphs | Engineering Design | Combinatorics | 05C35 | 05C38 | MATHEMATICS | GRAPHS | Upper bounds | Cages | Graph theory
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2019, Volume 39, Issue 3, pp. 731 - 740
A variant of the Lovász Conjecture on hamiltonian paths states that . Given a finite group and a connection set , the Cayley graph ) will be called if for... 
hamiltonian cycle | 05C45 | 05C99 | Cayley graph | normal connection set
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2019, Volume 35, Issue 6, pp. 1707 - 1714
It has been conjecture that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph... 
05C45 | 05C99 | Hamiltonian cycle | Mathematics | Engineering Design | Combinatorics | Cayley graph | Normal connection set | MATHEMATICS | Traveling salesman problem
Journal Article
Discrete Mathematics, ISSN 0012-365X, 10/2018, Volume 341, Issue 10, pp. 2694 - 2699
The anti-Ramsey number of Erdös, Simonovits and Sós from 1973 has become a classic invariant in Graph Theory. To extend this invariant to Matroid Theory, we... 
Hypergraph | Matroid | Anti-Ramsey number | MATHEMATICS | NUMBER
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2016, Volume 203, pp. 47 - 52
A digraph D=(V,A) is said to be m-colored if its arcs are colored with m colors. An m-colored digraph D has a k-colored kernel if there exists K⊆V such that... 
Colored-kernel | Kernel | Arc-coloring
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 9/2013, Volume 29, Issue 5, pp. 1517 - 1522
The heterochromatic number h c (H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k... 
Mathematics | Engineering Design | Combinatorics | Geometric graph | Matroid | Heterochromatic | MATHEMATICS | TREES | Geometry | Graphs | Planes | Color | Grounds | Colouring | Graph theory | Combinatorial analysis | Colour | Mathematics - Combinatorics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2017, Volume 37, Issue 2, pp. 301 - 313
An arc-coloured digraph D = (V,A) is said to be rainbow connected if for every pair {u, v} ⊆ V there is a directed uv-path all whose arcs have different... 
cactus | arc colouring | rainbow connectivity | Rainbow connectivity | Cactus | Arc-colouring | MATHEMATICS | arc-colouring
Journal Article
Discrete Mathematics, ISSN 0012-365X, 11/2016, Volume 339, Issue 11, pp. 2793 - 2803
In this paper we relate the global irregularity and the order of a c-partite tournament T to the existence of certain cycles and the problem of finding the... 
Multipartite tournaments | Cycles | Global irregularity | MATHEMATICS | Mathematical analysis | Irregularities
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2016, Volume 32, Issue 6, pp. 2199 - 2209
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by... 
Rainbow connected | Connectivity | Mathematics | Engineering Design | Combinatorics | Arc-colouring | MATHEMATICS | NUMBER | GRAPHS | Graphs | Graph theory | Rainbows | Combinatorial analysis | Color | Colour
Journal Article
Discrete Mathematics, ISSN 0012-365X, 04/2017, Volume 340, Issue 4, pp. 578 - 584
An arc-coloring of a strongly connected digraph D is a strongly monochromatic-connecting coloring if for every pair u,v of vertices in D there exist an... 
Coloring | Strong connectivity | Oriented graph | Monochromatic | MATHEMATICS | RAINBOW CONNECTION
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 07/2017, Volume 33, Issue 4, pp. 689 - 713
Let D be a connected oriented graph. A set is convex in D if, for every pair of vertices , the vertex set of every xy-geodesic, (xy shortest directed path) and... 
Convexity number | Convex set | Oriented graph | Grid | Spectrum | GRAPH | MATHEMATICS | GEODETIC NUMBER
Journal Article
Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 984 - 987
Let D=(V(D),A(D)) be a digraph, DP(D) be the set of directed paths of D and let Π be a subset of DP(D). A subset S⊆V(D) will be called Π-independent if for any... 
Richardson's theorem | Π-kernel
Journal Article
Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 984 - 987
Let D=(V(D),A(D)) be a digraph, DP(D) be the set of directed paths of D and let Π be a subset of DP(D). A subset S⊆V(D) will be called Π-independent if for any... 
[formula omitted]-kernel | Richardson’s theorem
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 3/2018, Volume 34, Issue 2, pp. 277 - 287
An edge colouring of a graph G is complete if for any distinct colours $$c_1$$ c1 and $$c_2$$ c2 one can find in G adjacent edges coloured with $$c_1$$ c1 and... 
Complete edge-colouring | Pseudoachromatic index | Complete graph | Finite projective plane | Mathematics | Complete colourings | Engineering Design | Combinatorics | 05C15 | 51E15 | MATHEMATICS | ACHROMATIC INDEX | Mathematics - Combinatorics
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2018, Volume 25, Issue 3
We consider the extension to directed graphs of the concept of the achromatic number in terms of acyclic vertex colorings. The achromatic number has been... 
COLORINGS | MATHEMATICS | MATHEMATICS, APPLIED | PSEUDOACHROMATIC INDEX | COMPLETE GRAPH | DICHROMATIC NUMBER | ACHROMATIC NUMBER
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2016, Volume 203, pp. 47 - 52
A digraph D=(V,A) is said to be m-colored if its arcs are colored with m colors. An m-colored digraph D has a k-colored kernel if there exists K⊆V such that... 
Colored-kernel | Kernel | Arc-coloring
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 01/2014, Volume 35, pp. 388 - 391
We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph. 
MATHEMATICS | MANIFOLDS | COCIRCUIT GRAPHS | Graphs | Vectors (mathematics) | Mathematical analysis | Combinatorial analysis | Computer Science
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 11/2014, Volume 34, Issue 4, pp. 651 - 671
A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph... 
k-quasi-transitive digraph | k-transitive digraph | digraph | Laborde-Payan-Xuong Conjecture | transitive digraph | quasi-transitive digraph | Transitive digraph | Quasi-transitive digraph | Digraph | Laborde-Payan-Xuong conjecture | MATHEMATICS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 09/2012, Volume 160, Issue 13-14, pp. 1971 - 1978
We study k -colored kernels in m -colored digraphs. An m -colored digraph D has k -colored kernel if there exists a subset K of its vertices such that 
Kernels | Mathematical analysis | Graph theory
Journal Article
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