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

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

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

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

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

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

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

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

(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

[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

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

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

We investigate some properties of lattice group-valued positive, monotone and k-subadditive set functions, and in particular, we give some comparisons between...

lattice group | filter (D)-convergence | Fremlin’s lemma | Vitali- -Hahn-Saks theorem | k-subadditive capacity | regular capacity | filter (O)-convergence | Maeda-Ogasawara-Vulikh theorem | Nikod´ym theorem | (s)-bounded capacity | limit theorem | Brooks-Jewett theorem | Dieudonn´e theorem | (diagonal) filter | continuous capacity | Fremlin's lemma | Dieudonńe theorem | Nikodým theorem | Vitali-Hahn-Saks theorem

lattice group | filter (D)-convergence | Fremlin’s lemma | Vitali- -Hahn-Saks theorem | k-subadditive capacity | regular capacity | filter (O)-convergence | Maeda-Ogasawara-Vulikh theorem | Nikod´ym theorem | (s)-bounded capacity | limit theorem | Brooks-Jewett theorem | Dieudonn´e theorem | (diagonal) filter | continuous capacity | Fremlin's lemma | Dieudonńe theorem | Nikodým theorem | Vitali-Hahn-Saks theorem

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

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

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

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

[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

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

Edge degree | Brooks' theorem | Graph coloring | Equitable coloring | MATHEMATICS | DENSE GRAPHS | H-FACTORS | PROOF

Journal Article

19.
Filter exhaustiveness and filter limit theorems for k-triangular lattice group-valued set functions

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

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

Brooks coloring theorem | Group colorings | Group connectivity | Nowhere-zero flows | MATHEMATICS | NOWHERE-ZERO 3-FLOWS | GRAPHS

Journal Article

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