Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, 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

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

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

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 Applied Mathematics, ISSN 0166-218X, 08/2014, Volume 173, pp. 102 - 112

In this paper, we initiate the study of complete colourings of oriented graphs and the new associated notion of the oriented achromatic number of oriented and...

Complete homomorphism | Achromatic number | Complete colouring | Oriented colouring | Oriented chromatic number | Elementary homomorphism | MATHEMATICS, APPLIED | CHROMATIC NUMBER | UNION | GRAPHS | Integers | Homomorphisms | Interpolation | Theorems | Mathematical analysis | Graphs | Colouring | Graph theory | Computer Science | Discrete Mathematics

Complete homomorphism | Achromatic number | Complete colouring | Oriented colouring | Oriented chromatic number | Elementary homomorphism | MATHEMATICS, APPLIED | CHROMATIC NUMBER | UNION | GRAPHS | Integers | Homomorphisms | Interpolation | Theorems | Mathematical analysis | Graphs | Colouring | Graph theory | 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

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 Mathematics, ISSN 0012-365X, 04/2019, 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

Oriented graph colouring | Oriented graph homomorphism | MATHEMATICS | CHROMATIC NUMBER | Computer Science | Discrete Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2018, 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

Caterpillar | Broadcast independence | Distance | Independence | GRAPH | MATHEMATICS, APPLIED | TREES | DOMINATION NUMBERS | TIME | EQUAL BROADCAST | Computer Science | Discrete Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2018, Volume 243, pp. 248 - 261

An arc-coloured path in a digraph is rainbow if its arcs have distinct colours. A vertex-coloured path is vertex rainbow if its internal vertices have distinct...

Rainbow connection | Rainbow vertex-connection | Total rainbow connection | Digraphs | MATHEMATICS, APPLIED | VERTEX-CONNECTION | HARDNESS | Computer Science | Discrete Mathematics

Rainbow connection | Rainbow vertex-connection | Total rainbow connection | Digraphs | MATHEMATICS, APPLIED | VERTEX-CONNECTION | HARDNESS | 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

05C12 | integer distance graph | 2-distance coloring | 05C15 | MATHEMATICS | PLANAR GRAPHS | GIRTH | 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

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

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

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

Discrete Applied Mathematics, ISSN 0166-218X, 11/2019, 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 | Trees (mathematics) | Graph theory | Graph coloring | Apexes | Upper bounds | Sums | Computer Science | Discrete Mathematics

Number of sums | Neighbour-sum-distinguishing edge-weightings | Trees (mathematics) | Graph theory | Graph coloring | Apexes | Upper bounds | Sums | Computer Science | Discrete Mathematics

Journal Article

Journal of Discrete Algorithms, ISSN 1570-8667, 03/2015, Volume 31, pp. 14 - 25

The incidence coloring game has been introduced in Andres (2009) [2] as a variation of the ordinary coloring game. The incidence game chromatic number ιg(G) of...

Incidence game chromatic number | [formula omitted]-decomposable graphs | Incidence coloring game | Arboricity | Incidence coloring | Arboricity (a, d) -decomposable graphs | Computer Science | Discrete Mathematics

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

Discrete Mathematics, ISSN 0012-365X, 07/2017, Volume 340, Issue 7, pp. 1564 - 1572

Let γ:E(G)⟶N∗=N∖{0} be an edge colouring of a graph G and σγ:V(G)⟶N∗ the vertex colouring given by σγ(v)=∑e∋vγ(e) for every v∈V(G). A...

Edge-weighting | Neighbour-sum-distinguishing edge-colouring game | Neighbour-sum-distinguishing edge-colouring | MATHEMATICS | VERSION | Computer Science | Discrete Mathematics

Edge-weighting | Neighbour-sum-distinguishing edge-colouring game | Neighbour-sum-distinguishing edge-colouring | MATHEMATICS | VERSION | 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

maximum average degree | incidence chromatic number | incidence coloring | planar graph | 05C15 | MATHEMATICS | STAR ARBORICITY | Computer Science | Discrete Mathematics | 05c15

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

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

Theoretical Computer Science, ISSN 0304-3975, 10/2018, 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

Combinatorial games | Graphs | Subtraction games | Octal games | COMPUTER SCIENCE, THEORY & METHODS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

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

homomorphism | coloring | oriented clique | planar graph | oriented graph

Journal Article

Discrete Mathematics and Theoretical Computer Science, ISSN 1365-8050, 2018, Volume 20, Issue 1, p. 6

We examine $t$-colourings of oriented graphs in which, for a fixed integer $k \geq 1$, vertices joined by a directed path of length at most $k$ must be...

G.2.2 | Computer Science - Discrete Mathematics | 05C15, 05C20, 05C60 | F.2.2 | Mathematics - Combinatorics | Computer Science | Discrete Mathematics

G.2.2 | Computer Science - Discrete Mathematics | 05C15, 05C20, 05C60 | F.2.2 | Mathematics - Combinatorics | 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

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

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