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Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 23, pp. 3426 - 3428
We give a proof of Brooks’ Theorem and its choosability extension based on the Alon–Tarsi Theorem; this also shows that Brooks’ Theorem remains valid in a more... 
Brooks’ Theorem | Alon–Tarsi method | Graph coloring | CIRCULAR CHOOSABILITY | MATHEMATICS | Brooks' Theorem | Alon-Tarsi method | Coloring | Theorems | Mathematical analysis | Games | Proving
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 11/2015, Volume 80, Issue 3, pp. 199 - 225
We collect some of our favorite proofs of Brooks' Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques... 
graph coloring | Kempe chains | list coloring | hitting sets | Brooks Theorem | COLORINGS | MATHEMATICS | SHORT PROOFS | DELTA | CHROMATIC NUMBER | EFFECTIVE VERSION | GRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 12/2010, Volume 310, Issue 23, pp. 3426 - 3428
We give a proof of Brooks' Theorem and its choosability extension based on the AlonTarsi Theorem; this also shows that Brooks' Theorem remains valid in a more... 
Brooks' Theorem | AlonTarsi method | Graph coloring
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 06/2019, Volume 91, Issue 2, pp. 148 - 161
Dvořák and Postle introduced DP‐coloring of simple graphs as a generalization of list‐coloring. They proved a Brooks' type theorem for DP‐coloring; and... 
list‐coloring | coloring | DP‐coloring | Brooks' type theorem | list-coloring | DP-coloring | MATHEMATICS | GRAPHS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 02/2015, Volume 338, Issue 2, pp. 272 - 273
Brooks’ theorem is a fundamental result in the theory of graph coloring. Catlin proved the following strengthening of Brooks’ theorem: Let d be an integer at... 
Catlin’s theorem | Independent set | Chromatic number | Brooks’ theorem
Journal Article
Discrete Mathematics, ISSN 0012-365X, 02/2015, Volume 338, Issue 2, pp. 272 - 273
Brooks' theorem is a fundamental result in the theory of graph coloring. Catlin proved the following strengthening of Brooks' theorem: Let d be an integer at... 
Catlin's theorem | Independent set | Brooks' theorem | Chromatic number | MATHEMATICS | Integers | Strengthening | Theorems | Graph coloring | Mathematical analysis | Proving | Color | Graphs
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 12/2016, Volume 83, Issue 4, pp. 340 - 358
Let G be a simple undirected connected graph on n vertices with maximum degree Δ. Brooks' Theorem states that G has a proper Δ‐coloring unless G is a complete... 
reconfigurations | Brooks’ Theorem | graph coloring | LIST EDGE-COLORINGS | GRAPH | MATHEMATICS | Brooks' Theorem | COMPLEXITY
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 12/2015, Volume 80, Issue 4, pp. 277 - 286
A classical theorem of Brooks in graph coloring theory states that every connected graph G has its chromatic number χ(G) less than or equal to its maximum... 
(k,l)‐colouring | Bichromatic Number | Brooks' Theorem | (k,l)-colouring | MATHEMATICS | DISTANCE | HEREDITARY | INDEPENDENT SETS | CLIQUES | GRAPHS
Journal Article
Information Processing Letters, ISSN 0020-0190, 2012, Volume 112, Issue 5, pp. 200 - 204
The well-known Brooksʼ Theorem says that each graph G of maximum degree k ⩾ 3 is k-colorable unless G = K k + 1 . We generalize this theorem by allowing higher... 
[formula omitted]-diamond | [formula omitted]-dart graph | Graph algorithms | NP-complete problem | Brooksʼ Theorem | (k, s) -dart graph | (k, s) -diamond | Brooks Theorem | COMPUTER SCIENCE, INFORMATION SYSTEMS | Brooks' Theorem | (k, s)-dart graph | (k, s)-diamond | Graphs | Theorems
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2014, Volume 325, Issue 1, pp. 12 - 16
We prove that for k≥3, the chromatic number of k-th powers of graphs of maximum degree Δ≥3 can be bounded in a more refined way than with Brooks’ theorem, even... 
Coloring | Powers | Brooks | MATHEMATICS | Mathematics | Combinatorics | Computer Science | Discrete Mathematics
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 03/2018, Volume 25, Issue 1
For a graph G, let chi(G) and lambda(G) denote the chromatic number of G and the maximum local edge connectivity of G, respectively. A result of Dirac implies... 
Connectivity | Graph coloring | Critical graphs | Brooks’ theorem | MATHEMATICS | MATHEMATICS, APPLIED | connectivity | graph coloring | Brooks' theorem | critical graphs | GRAPHS
Journal Article
Tatra Mountains Mathematical Publications, ISSN 1210-3195, 03/2016, Volume 65, Issue 1, pp. 1 - 21
Journal Article
KYBERNETIKA, ISSN 0023-5954, 2019, Volume 55, Issue 2, pp. 233 - 251
Some versions of Dieudonne-type convergence and uniform boundedness theorems are proved, for k-triangular and regular lattice group-valued set functions. We... 
lattice group | (s)-bounded set function | k-triangular set function | (D)-convergence | limit theorem | Brooks-Jewett theorem | COMPUTER SCIENCE, CYBERNETICS | RESPECT | FILTER CONVERGENCE | LIMIT-THEOREMS | Fremlin lemma | Nikodym boundedness theorem | BOUNDEDNESS THEOREM | Dieudonne theorem
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 2019
The vertex-arboricity aG of a graph G is the minimum number of subsets that the vertices of G can be partitioned so that the subgraph induced by each set of... 
Degeneracy | Vertex coloring | Brooks’ Theorem | Vertex arboricity
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2012, Volume 26, Issue 2, pp. 452 - 471
Let Delta(G) be the maximum degree of a graph G. Brooks' theorem states that the only connected graphs with chromatic number chi(G) = Delta(G) + 1 are complete... 
Chromatic number | Fractional chromatic number | Brooks' theorem | MATHEMATICS, APPLIED | chromatic number | fractional chromatic number
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 355, Issue 2, pp. 839 - 845
In classical measure theory the Brooks–Jewett Theorem provides a finitely-additive-analogue to the Vitali–Hahn–Saks Theorem. In this paper, it is studied... 
[formula omitted]-algebra | Vitali–Hahn–Saks property | Brooks–Jewett property | von Neumann algebra | Brooks-Jewett property | algebra | Vitali-Hahn-Saks property | MATHEMATICS | MATHEMATICS, APPLIED | WEAKLY COMPACT-OPERATORS | SPACES | CSTAR-ALGEBRAS | ASTERISK-ALGEBRAS | C-algebra | Universities and colleges
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2011, Volume 311, Issue 17, pp. 1995 - 1997
In this paper, I present a new structural lemma for k -regular graphs, similar to an earlier lemma by Lovász (1975)  [5]. The new lemma is then used to give an... 
List-colouring | [formula omitted]-regular graphs | Graph colouring | Brooks’ theorem | Brooks' theorem | k-regular graphs | MATHEMATICS | Graphs | Theorems | Algebra | Mathematical analysis | Proving
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 2009, Volume 99, Issue 2, pp. 298 - 305
The Ore-degree of an edge xy in a graph G is the sum θ ( x y ) = d ( x ) + d ( y ) of the degrees of its ends. In this paper we discuss colorings and equitable... 
Edge degree | Brooks' theorem | Graph coloring | Equitable coloring | MATHEMATICS | DENSE GRAPHS | H-FACTORS | PROOF
Journal Article
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, ISSN 1120-6330, 2019, Volume 30, Issue 2, pp. 379 - 389
We give some limit theorems for sequences of lattice group-valued k-triangular set functions, in the setting of filter convergence, and some results about... 
Lattice group | MATHEMATICS, APPLIED | k-triangular set function | filter order convergence | filter | MATHEMATICS | BROOKS-JEWETT | VITALI-HAHN-SAKS | CONVERGENCE | filter exhaustiveness | submeasure | TOPOLOGICAL RINGS | Frechet-Nikodym topology
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2012, Volume 312, Issue 15, pp. 2294 - 2303
Let G be a 2-edge-connected undirected graph, A be an (additive) Abelian group, and A∗=A−{0}. A graph G is A-connected if G has an orientation D(G) such that... 
Brooks coloring theorem | Group colorings | Group connectivity | Nowhere-zero flows | MATHEMATICS | NOWHERE-ZERO 3-FLOWS | GRAPHS
Journal Article
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