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Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 266, pp. 219 - 236
A distinguishing r-labelling of a digraph G is a mapping λ from the set of vertices of G to the set of labels {1,…,r} such that no nontrivial automorphism of G... 
Albertson–Collins Conjecture | Automorphism group | Cyclic tournament | Distinguishing number | MATHEMATICS, APPLIED | Albertson-Collins Conjecture | AUTOMORPHISMS | POWERS | CARTESIAN PRODUCTS | GRAPHS | Supermarkets | Apexes | Labelling | Mapping | Labels | Graph theory | Tournaments & championships | Labeling | Automorphisms | Computer Science | Discrete Mathematics
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 05/2016, Volume 627, pp. 90 - 101
Given two finite sets of integers S⊆N∖{0} and D⊆N∖{0,1}, the impartial combinatorial game i-Mark(S,D) is played on a heap of tokens. From a heap of n tokens,... 
Combinatorial games | Subtraction division games | Sprague–Grundy sequence | Aperiodicity | Subtraction games | Sprague-Grundy sequence | Integers | Conventions | Computation | Integrals | Mathematical analysis | Games | Combinatorial analysis | Players | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2019, Volume 265, pp. 40 - 55
An incidence of a graph G is a pair (v,e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v,e) and (w,f) of G are adjacent... 
Incidence colouring | List colouring | Hamiltonian cubic graph | Incidence list colouring | Square grid | Halin graph | INCIDENCE CHROMATIC NUMBER | MATHEMATICS, APPLIED | INCIDENCE COLORING CONJECTURE | Coloring | Graphs | Mapping | Upper bounds | Incidence | Computer Science | Discrete Mathematics
Journal Article
Discrete mathematics, ISSN 0012-365X, 2019, Volume 342, Issue 4, pp. 959 - 974
We show that any orientation of a graph with maximum degree three has an oriented 9-colouring, and that any orientation of a graph with maximum degree four has... 
Oriented graph colouring | Oriented graph homomorphism | MATHEMATICS | CHROMATIC NUMBER | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2018, Volume 251, Issue 83-92, pp. 83 - 92
The 1–2–3 Conjecture asks whether every graph with no connected component isomorphic to K2 can be 3-edge-weighted so that every two adjacent vertices u and v... 
1–2–3 Conjecture | Difference-2 distinction | Bipartite graphs | 1-2-3 Conjecture | MATHEMATICS, APPLIED | Algorithms | Weighting | Applied mathematics | Apexes | Weights & measures | Graphs | Graph theory | Polynomials | Sums | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 270, pp. 13 - 24
Neighbour-sum-distinguishing edge-weightings are a way to “encode” proper vertex-colourings via the sums of weights incident to the vertices. Over the last... 
Number of sums | Neighbour-sum-distinguishing edge-weightings | Neighbour-sum-distinguishing | edge-weightings | MATHEMATICS, APPLIED | COMPLEXITY | Trees (mathematics) | Graph theory | Graph coloring | Apexes | Upper bounds | Sums | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2018, Volume 244, pp. 20 - 35
Let G be a simple undirected graph. A broadcast on G is a function f:V(G)→N such that f(v)≤eG(v) holds for every vertex v of G, where eG(v) denotes the... 
Caterpillar | Broadcast independence | Distance | Independence | GRAPH | MATHEMATICS, APPLIED | TREES | DOMINATION NUMBERS | TIME | EQUAL BROADCAST | Computer Science | Discrete Mathematics
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 07/2015, Volume 79, Issue 3, pp. 178 - 212
A signed graph [G,Σ] is a graph G together with an assignment of signs + and − to all the edges of G where Σ is the set of negative edges. Furthermore [G,Σ1]... 
homomorphism | signed graph | coloring | minor | Hadwiger's conjecture | PROJECTIVE CUBES | COLORINGS | MATHEMATICS | EDGE-COLORED GRAPHS | PLANAR GRAPHS | FLOWS | CONJECTURE | Computer Science | Discrete Mathematics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 589 - 603
A 2-distance -coloring of a graph is a mapping from ( ) to the set of colors {1,. . ., } such that every two vertices at distance at most 2 receive distinct... 
05C12 | integer distance graph | 2-distance coloring | 05C15 | MATHEMATICS | PLANAR GRAPHS | GIRTH | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 222, pp. 40 - 53
With any (not necessarily proper) edge k-colouring γ:E(G)⟶{1,…,k} of a graph G, one can associate a vertex colouring σγ given by σγ(v)=∑e∋vγ(e). A... 
Neighbour-sum-distinguishing edge colouring | Equitable colouring | Neighbour-sum-distinguishing total colouring | MATHEMATICS, APPLIED | VERTEX | WEIGHTINGS | GRAPHS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics
Journal Article
Journal of Discrete Algorithms, ISSN 1570-8667, 03/2015, Volume 31, pp. 14 - 25
.... In Charpentier and Sopena (2013) [7], we proved that ιg(G)≤⌊3Δ(G)−a2⌋+8a−1 for every graph G with arboricity at most a... 
Incidence game chromatic number | [formula omitted]-decomposable graphs | Incidence coloring game | Arboricity | Incidence coloring | Arboricity (a, d) -decomposable graphs | Computer Science | Discrete Mathematics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 345 - 354
An in a graph is a pair ( ) where is a vertex of and is an edge of incident to . Two incidences ( ) and ( ) are adjacent if at least one of the following... 
maximum average degree | incidence chromatic number | incidence coloring | planar graph | 05C15 | MATHEMATICS | STAR ARBORICITY | Computer Science | Discrete Mathematics | 05c15
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 06/2016, Volume 82, Issue 2, pp. 165 - 193
The clique number of an undirected graph G is the maximum order of a complete subgraph of G and is a well‐known lower bound for the chromatic number of G.... 
homomorphism | coloring | oriented clique | planar graph | oriented graph
Journal Article
Theoretical computer science, ISSN 0304-3975, 2018, Volume 746, pp. 19 - 35
Octal games are a well-defined family of two-player games played on heaps of counters, in which the players remove alternately a certain number of counters... 
Combinatorial games | Graphs | Subtraction games | Octal games | COMPUTER SCIENCE, THEORY & METHODS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2017, Volume 37, Issue 3, pp. 665 - 690
The packing chromatic number χ ) of a graph is the smallest integer such that its set of vertices ) can be partitioned into disjoint subsets , . . . , , in... 
path | packing chromatic number | packing coloring | 05C70 | corona graph | cycle | 05C05 | 05C15 | Path | Packing chromatic number | Corona graph | Packing coloring | Cycle | MATHEMATICS | CHROMATIC NUMBER | Computer Science | Discrete Mathematics
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 17, pp. 2327 - 2333
The square G 2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most 2 in G are joined by an edge. We study... 
Cartesian product of cycles | Distance-2 coloring | Square of graphs | Chromatic number | PATH | MATHEMATICS | NUMBER | PLANAR GRAPH | L(2,1)-LABELINGS | L(D | Cartesian | Coloring | Graphs | Ceilings | Mathematical analysis | Edge joints | Computer Science | Discrete Mathematics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 179, pp. 69 - 78
An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection... 
Rainbow connection | Tournaments | Digraphs | MATHEMATICS, APPLIED | MINIMUM DEGREE
Journal Article
Journal Article
Australasian Journal of Combinatorics, ISSN 1034-4942, 2016, Volume 66, Issue 2, pp. 310 - 329
Journal Article
Journal of Discrete Algorithms, ISSN 1570-8667, 01/2015, Volume 30, pp. 113 - 127
An undirected simple graph G is locally irregular if adjacent vertices of G have different degrees. An edge-colouring ϕ of G is locally irregular if each... 
Irregular chromatic index | Irregular graph | Locally irregular graph | Edge-colouring | Computer Science | Discrete Mathematics
Journal Article
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