Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 12, pp. 2034 - 2037

The adjacent vertex-distinguishing chromatic index χ a ′ ( G ) of a graph G is the smallest integer k for which G admits a proper edge k -coloring such that...

Adjacent vertex-distinguishing edge coloring | Maximum degree | [formula omitted]-minor free graph | minor free graph | MATHEMATICS, APPLIED | K-4-minor free graph

Adjacent vertex-distinguishing edge coloring | Maximum degree | [formula omitted]-minor free graph | minor free graph | MATHEMATICS, APPLIED | K-4-minor free graph

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 223, pp. 52 - 63

A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study cubic graphs whose vertex...

Total domination | Claw-free | Vertex partitions | [formula omitted]-chordal graphs | 5-chordal graphs | 2-COLORINGS | MATHEMATICS, APPLIED | CHORDALITY | HYPERGRAPHS

Total domination | Claw-free | Vertex partitions | [formula omitted]-chordal graphs | 5-chordal graphs | 2-COLORINGS | MATHEMATICS, APPLIED | CHORDALITY | HYPERGRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 12/2016, Volume 339, Issue 12, pp. 3085 - 3088

A graph G is said to be K1,r-free if G does not contain an induced subgraph isomorphic to K1,r. Let k, r be integers with k≥2, r≥4. In this paper, we prove...

Vertex-disjoint stars | [formula omitted]-free graph | Minimum degree | free graph

Vertex-disjoint stars | [formula omitted]-free graph | Minimum degree | free graph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 11/2015, Volume 338, Issue 11, pp. 1982 - 1988

Let T be a 3-partite tournament and F3(T) be the set of vertices of T not in triangles. We prove that, if the global irregularity of T, ig(T), is one and...

Tripartite tournaments | [formula omitted]-free vertices | Global irregularity | C 3 →-free vertices | MATHEMATICS | MULTIPARTITE TOURNAMENTS | (C-3)over-right-arrow-free vertices

Tripartite tournaments | [formula omitted]-free vertices | Global irregularity | C 3 →-free vertices | MATHEMATICS | MULTIPARTITE TOURNAMENTS | (C-3)over-right-arrow-free vertices

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2017, Volume 340, Issue 4, pp. 649 - 654

A graph G is said to be K1,r-free if G does not contain an induced subgraph isomorphic to K1,r. Let k,r,t be integers with k≥2 and t≥3. In this paper, we prove...

Vertex-disjoint stars | [formula omitted]-free graph | Minimum degree | free graph

Vertex-disjoint stars | [formula omitted]-free graph | Minimum degree | free graph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2015, Volume 338, Issue 10, pp. 1674 - 1680

A vertex v in a graph G is called α-redundant if α(G−v)=α(G), where α(G) stands for the independence number of G, i.e. the maximum size of a subset of pairwise...

Stability number | [formula omitted]-redundant | Graph reduction | Graph transformation | Maximum independent set | Stable set | Independence number | α-redundant | TERMS | ALGORITHMS | INDEPENDENT SETS | P-5-FREE GRAPHS | MATHEMATICS | LOWER BOUNDS | alpha-redundant | STABLE SET PROBLEM | P-6

Stability number | [formula omitted]-redundant | Graph reduction | Graph transformation | Maximum independent set | Stable set | Independence number | α-redundant | TERMS | ALGORITHMS | INDEPENDENT SETS | P-5-FREE GRAPHS | MATHEMATICS | LOWER BOUNDS | alpha-redundant | STABLE SET PROBLEM | P-6

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2019, Volume 517, pp. 396 - 438

Given a finite-dimensional reductive Lie algebra g equipped with a nondegenerate, invariant, symmetric bilinear form B, let Vk(g,B) denote the universal affine...

[formula omitted]-algebra | Finite generation | Commutant construction | Orbifold construction | Invariant theory | [formula omitted] superconformal algebra | Affine vertex algebra | Coset construction | N=2 superconformal algebra | W-algebra | FUSION RULES | REPRESENTATIONS | EXTENSIONS | W1+INFINITY | KAC-MOODY ALGEBRAS | DIMENSIONAL LIE-ALGEBRAS | SUBALGEBRAS | CATEGORIES | MATHEMATICS | W-ALGEBRAS | CONSTRUCTION | Algebra | Electric generators

[formula omitted]-algebra | Finite generation | Commutant construction | Orbifold construction | Invariant theory | [formula omitted] superconformal algebra | Affine vertex algebra | Coset construction | N=2 superconformal algebra | W-algebra | FUSION RULES | REPRESENTATIONS | EXTENSIONS | W1+INFINITY | KAC-MOODY ALGEBRAS | DIMENSIONAL LIE-ALGEBRAS | SUBALGEBRAS | CATEGORIES | MATHEMATICS | W-ALGEBRAS | CONSTRUCTION | Algebra | Electric generators

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2015, Volume 184, pp. 114 - 121

In VCP4 problem, it is asked to find a set S⊆V of minimum size such that G[V∖S] contains no path on 4 vertices, in a given graph G=(V,E). We prove that it is...

[formula omitted]-free graph | Approximation algorithm | [formula omitted] vertex cover | Regular graph

[formula omitted]-free graph | Approximation algorithm | [formula omitted] vertex cover | Regular graph

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2012, Volume 160, Issue 7-8, pp. 1285 - 1290

Let G be a graph of order n(G), minimum degree δ(G) and connectivity κ(G). We call the graph Gmaximally connected when κ(G)=δ(G). The graph G is said to be...

Diamond-free graphs | Connectivity | Vertex transitive graphs | [formula omitted]-diamond-free graphs | Superconnected | p-diamond-free graphs | MATHEMATICS, APPLIED | DIGRAPHS

Diamond-free graphs | Connectivity | Vertex transitive graphs | [formula omitted]-diamond-free graphs | Superconnected | p-diamond-free graphs | MATHEMATICS, APPLIED | DIGRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2018, Volume 239, pp. 119 - 124

For a set H of graphs, a graph G is H-free if G does not contain any subgraph isomorphic to some graph in H. In this paper, we study the minimum H-free node...

Node deletion problem | Local search | PTAS | Degree-bounded node deletion | Disk graph | Maximum subgraph problem | Connected [formula omitted]-subgraph cover | [formula omitted]-path vertex cover | Connected k-subgraph cover | k-path vertex cover | MATHEMATICS, APPLIED | SET | PATH VERTEX COVER | P-3 PROBLEM | APPROXIMATION ALGORITHM | CUBIC GRAPHS | BIPARTITE GRAPHS

Node deletion problem | Local search | PTAS | Degree-bounded node deletion | Disk graph | Maximum subgraph problem | Connected [formula omitted]-subgraph cover | [formula omitted]-path vertex cover | Connected k-subgraph cover | k-path vertex cover | MATHEMATICS, APPLIED | SET | PATH VERTEX COVER | P-3 PROBLEM | APPROXIMATION ALGORITHM | CUBIC GRAPHS | BIPARTITE GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 19, pp. 2499 - 2503

A graph is said to be K 1 , t -free if it does not contain an induced subgraph isomorphic to K 1 , t . Let h ( t , k ) be the smallest integer m such that...

Triangle | Disjoint | [formula omitted]-free graph | Ramsey number

Triangle | Disjoint | [formula omitted]-free graph | Ramsey number

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2017, Volume 340, Issue 6, pp. 1210 - 1226

Line graphs constitute a rich and well-studied class of graphs. In this paper, we focus on three different topics related to line graphs of subcubic...

Min-max theorems | [formula omitted]-completeness | Line graph | Approximation hardness | Independence number | Matching number | NP-completeness | CLAW | RATIO | MATCHINGS | HAMILTONIAN PATH PROBLEM | INDEPENDENT SETS | FEEDBACK VERTEX SET | MATHEMATICS | K-4)-FREE 4-REGULAR GRAPHS | CYCLES | PLANAR GRAPHS | Computer Science | Discrete Mathematics

Min-max theorems | [formula omitted]-completeness | Line graph | Approximation hardness | Independence number | Matching number | NP-completeness | CLAW | RATIO | MATCHINGS | HAMILTONIAN PATH PROBLEM | INDEPENDENT SETS | FEEDBACK VERTEX SET | MATHEMATICS | K-4)-FREE 4-REGULAR GRAPHS | CYCLES | PLANAR GRAPHS | Computer Science | Discrete Mathematics

Journal Article

Information and Computation, ISSN 0890-5401, 04/2017, Volume 253, pp. 109 - 126

Given a graph G and integers k1, k2, and k3, the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k1...

Forbidden induced subgraph | Proper Helly circular-arc graph | (Proper, unit) interval model | {Claw, [formula omitted], [formula omitted]}-free graph | Certifying algorithm | Graph modification problem | (Proper, Helly) arc model | C | Claw, S | free graph | MATHEMATICS, APPLIED | CIRCULAR-ARC GRAPHS | (Proper,unit) interval model | LINEAR-TIME | (Proper,Helly) arc model | {Claw,S-3, (S)over-bar, C-4}-free graph | VERTEX DELETION | COMPUTER SCIENCE, THEORY & METHODS | COMPLETION | HEREDITARY PROPERTIES | Algorithms

Forbidden induced subgraph | Proper Helly circular-arc graph | (Proper, unit) interval model | {Claw, [formula omitted], [formula omitted]}-free graph | Certifying algorithm | Graph modification problem | (Proper, Helly) arc model | C | Claw, S | free graph | MATHEMATICS, APPLIED | CIRCULAR-ARC GRAPHS | (Proper,unit) interval model | LINEAR-TIME | (Proper,Helly) arc model | {Claw,S-3, (S)over-bar, C-4}-free graph | VERTEX DELETION | COMPUTER SCIENCE, THEORY & METHODS | COMPLETION | HEREDITARY PROPERTIES | Algorithms

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2013, Volume 313, Issue 20, pp. 2348 - 2353

The acyclic disconnection ω⃗(D) of a digraph D is defined as the maximum number of colors in a coloring of the vertices of D such that no cycle is properly...

[formula omitted]-free disconnection | Acyclic disconnection | Vertex coloring | Tournament

[formula omitted]-free disconnection | Acyclic disconnection | Vertex coloring | Tournament

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2013, Volume 313, Issue 5, pp. 715 - 720

A graph is 2P3-free if it does not contain two vertex-disjoint paths on three vertices as an induced subgraph. We prove that every triangle-free 2P3-free graph...

[formula omitted]-free graph | Vertex coloring | Chromatic number | Triangle-free graph | 2p3 -free graph

[formula omitted]-free graph | Vertex coloring | Chromatic number | Triangle-free graph | 2p3 -free graph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 20, pp. 2735 - 2741

It is proved that if G is a k -connected K 1 , 4 -free graph and S is a subset of vertices such that k ≥ 3 and | S | ≤ 2 k then G has a cycle containing S . A...

[formula omitted]-free graph | Cyclability | [formula omitted]-connected graph | Subset of vertices

[formula omitted]-free graph | Cyclability | [formula omitted]-connected graph | Subset of vertices

Journal Article

Computer-Aided Design, ISSN 0010-4485, 2009, Volume 41, Issue 11, pp. 812 - 824

This paper enhances the conventional parametric algorithms for polyhedron blending, by strategically inverting the edges-first approach to vertex-first, so...

Parametric blending | Vertex blending | [formula omitted]-patches | Blending functions | Bézier surfaces | S-patches | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Bezier surfaces | POINTS | SURFACES

Parametric blending | Vertex blending | [formula omitted]-patches | Blending functions | Bézier surfaces | S-patches | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Bezier surfaces | POINTS | SURFACES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2017, Volume 314, pp. 71 - 123

We give new proofs of the rationality of the N=1 superconformal minimal model vertex operator superalgebras and of the classification of their modules in both...

Jack symmetric functions | Vertex operator super algebra | [formula omitted] superconformal algebra | Zhu algebra | N=1 superconformal algebra | INVARIANCE | VIRASORO ALGEBRA | VERMA MODULES | SINGULAR VECTORS | CHARACTERS | MATHEMATICS | REPRESENTATION-THEORY | CALOGERO-SUTHERLAND MODEL | VERTEX OPERATOR-ALGEBRAS | NEVEU-SCHWARZ | 2 DIMENSIONS | Analysis | Algebra

Jack symmetric functions | Vertex operator super algebra | [formula omitted] superconformal algebra | Zhu algebra | N=1 superconformal algebra | INVARIANCE | VIRASORO ALGEBRA | VERMA MODULES | SINGULAR VECTORS | CHARACTERS | MATHEMATICS | REPRESENTATION-THEORY | CALOGERO-SUTHERLAND MODEL | VERTEX OPERATOR-ALGEBRAS | NEVEU-SCHWARZ | 2 DIMENSIONS | Analysis | Algebra

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2018

Strictly Chordality-k graphs (SC graphs) are graphs which are either cycle free or every induced cycle is exactly k, for some fixed k,k≥3. Note that k=3 and...

Girth = chordality = k | Minimal vertex separator | Treewidth

Girth = chordality = k | Minimal vertex separator | Treewidth

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2012, Volume 312, Issue 2, pp. 324 - 330

We characterize the class of claw-free b -perfect graphs by giving a complete description of their structure.

Vertex coloring | [formula omitted]-perfect graph | [formula omitted]-coloring | Claw-free graph | b-perfect graph | b-coloring | MATHEMATICS | CHROMATIC NUMBER | Mathematical analysis | Graphs | Computer Science | Discrete Mathematics

Vertex coloring | [formula omitted]-perfect graph | [formula omitted]-coloring | Claw-free graph | b-perfect graph | b-coloring | MATHEMATICS | CHROMATIC NUMBER | Mathematical analysis | Graphs | Computer Science | Discrete Mathematics

Journal Article

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