Information Processing Letters, ISSN 0020-0190, 12/2019, Volume 152, p. 105838

•We study the fractional factor problems, which have wide-range applications in many areas.•We first define the fractional (a,b,k)-critical covered graph.•We...

Fractional [formula omitted]-factor | Combinatorial problems | Fractional [formula omitted]-critical covered graph | Degree condition | Fractional [formula omitted]-covered graph | Fractional [a, b]-factor | Fractional (a, b, k)-critical covered graph | COMPUTER SCIENCE, INFORMATION SYSTEMS | Fractional [a, b]-covered graph | ORTHOGONAL FACTORIZATIONS | TOUGHNESS CONDITION

Fractional [formula omitted]-factor | Combinatorial problems | Fractional [formula omitted]-critical covered graph | Degree condition | Fractional [formula omitted]-covered graph | Fractional [a, b]-factor | Fractional (a, b, k)-critical covered graph | COMPUTER SCIENCE, INFORMATION SYSTEMS | Fractional [a, b]-covered graph | ORTHOGONAL FACTORIZATIONS | TOUGHNESS CONDITION

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2018, Volume 250, pp. 47 - 56

Let γg(G) be the game domination number of a graph G. For any vertex v∈V(G), we denote by G|v a partially dominated graph G in which the vertex v is already...

Game domination number | [formula omitted]-edge-critical graph | [formula omitted]-stable graph | Domination game | [Formula presented]-edge-critical graph | [Formula presented]-stable graph | MATHEMATICS, APPLIED | 3/5-CONJECTURE | TREES | gamma(g)-stable graph | EXTREMAL FAMILIES | gamma(g)-edge-critical graph

Game domination number | [formula omitted]-edge-critical graph | [formula omitted]-stable graph | Domination game | [Formula presented]-edge-critical graph | [Formula presented]-stable graph | MATHEMATICS, APPLIED | 3/5-CONJECTURE | TREES | gamma(g)-stable graph | EXTREMAL FAMILIES | gamma(g)-edge-critical graph

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 06/2019, Volume 263, pp. 212 - 219

Let e be an edge of a connected simple graph G. The graph obtained by removing (resp. subdividing) an edge e from G is denoted by G−e (resp. Ge). As usual,...

[formula omitted]-critical graph | Domination number | Tree | [formula omitted]-insensitive graph | Edge removing | Efficient graph | Edge subdividing | Vizing’s Conjecture | Vizing's Conjecture | γ-insensitive graph | critical graph | MATHEMATICS, APPLIED | gamma(sd)-critical graph | gamma-insensitive graph | Graphs

[formula omitted]-critical graph | Domination number | Tree | [formula omitted]-insensitive graph | Edge removing | Efficient graph | Edge subdividing | Vizing’s Conjecture | Vizing's Conjecture | γ-insensitive graph | critical graph | MATHEMATICS, APPLIED | gamma(sd)-critical graph | gamma-insensitive graph | Graphs

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2019, Volume 342, Issue 6, pp. 1613 - 1623

Let G be a simple graph, and let Δ(G), d¯(G) and χ′(G) denote the maximum degree, the average degree and the chromatic index of G, respectively. We called...

Edge-[formula omitted]-coloring | Vizing’s adjacency lemma | Edge-critical graphs | Edge-k-coloring | Vizing's adjacency lemma | MATHEMATICS | SIZE

Edge-[formula omitted]-coloring | Vizing’s adjacency lemma | Edge-critical graphs | Edge-k-coloring | Vizing's adjacency lemma | MATHEMATICS | SIZE

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 12, pp. 4144 - 4148

Let G be a graph, and let a , b and k be nonnegative integers with 1 ≤ a ≤ b . An [ a , b ] -factor of graph G is defined as a spanning subgraph F of G such...

Connectivity | Graph | [formula omitted]-critical graph | Independence number | [formula omitted]-factor | [a, b]-factor | (a, b, k)-critical graph | MATHEMATICS | vertical bar a, b vertical bar-factor

Connectivity | Graph | [formula omitted]-critical graph | Independence number | [formula omitted]-factor | [a, b]-factor | (a, b, k)-critical graph | MATHEMATICS | vertical bar a, b vertical bar-factor

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 142 - 148

A graph is k-critical if it is k-chromatic but each of its proper induced subgraphs is (k−1)-colorable. It is known that the number of 4-critical P5-free...

[formula omitted]-free graphs | Graph coloring | free graphs | MATHEMATICS, APPLIED | 3-COLORABILITY | P-5-free graphs | K-COLORABILITY | Computer Science | Discrete Mathematics

[formula omitted]-free graphs | Graph coloring | free graphs | MATHEMATICS, APPLIED | 3-COLORABILITY | P-5-free graphs | K-COLORABILITY | Computer Science | Discrete Mathematics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2019, Volume 342, Issue 8, pp. 2308 - 2314

In this article, we obtain a sufficient condition related to toughness τ(G) for a graph to be all fractional (a,b,k)-critical. We prove that if τ(G)≥(b2−1)+aka...

All fractional [formula omitted]-critical graph | Toughness | Graph | Network | MATHEMATICS | INDEPENDENCE NUMBER | All fractional (a, b, k)-critical graph | CONNECTIVITY | ORTHOGONAL FACTORIZATIONS | F)-FACTORS

All fractional [formula omitted]-critical graph | Toughness | Graph | Network | MATHEMATICS | INDEPENDENCE NUMBER | All fractional (a, b, k)-critical graph | CONNECTIVITY | ORTHOGONAL FACTORIZATIONS | F)-FACTORS

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 9, pp. 1533 - 1538

Let G be a graph, and k a positive integer. Let h : E ( G ) → [ 0 , 1 ] be a function. If ∑ e ∋ x h ( e ) = k holds for each x ∈ V ( G ) , then we call G [ F h...

Fractional [formula omitted]-factor | Fractional [formula omitted]-deleted graph | Binding number | Graph | [formula omitted]-factor | Fractional k-factor | k-factor | Fractional (k,m)-deleted graph | EXISTENCE | MATHEMATICS, APPLIED | K)-CRITICAL GRAPHS | K-FACTORS | Fractional (k. m)-deleted graph | Binding | Integers | Graphs | Mathematical analysis | Indicators

Fractional [formula omitted]-factor | Fractional [formula omitted]-deleted graph | Binding number | Graph | [formula omitted]-factor | Fractional k-factor | k-factor | Fractional (k,m)-deleted graph | EXISTENCE | MATHEMATICS, APPLIED | K)-CRITICAL GRAPHS | K-FACTORS | Fractional (k. m)-deleted graph | Binding | Integers | Graphs | Mathematical analysis | Indicators

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 02/2015, Volume 182, pp. 91 - 98

With respect to a hereditary class C of graphs, a k-chromatic graph G∈C is said to be k-critical if every proper subgraph of G belonging to C is k−1 colorable....

Graph coloring | Critical graphs | [formula omitted]-free graphs

Graph coloring | Critical graphs | [formula omitted]-free graphs

Journal Article

Information Processing Letters, ISSN 0020-0190, 2009, Volume 109, Issue 14, pp. 811 - 815

Let G be a graph of order p, and let a , b and n be nonnegative integers with b ⩾ a ⩾ 2 , and let f be an integer-valued function defined on V ( G ) such that...

Fractional f-factor | Combinatorial problems | Binding number | Fractional [formula omitted]-critical graph | Graph | Fractional (f, n)-critical graph | EXISTENCE | (G,F)-FACTORS | COMPUTER SCIENCE, INFORMATION SYSTEMS | K-FACTORS

Fractional f-factor | Combinatorial problems | Binding number | Fractional [formula omitted]-critical graph | Graph | Fractional (f, n)-critical graph | EXISTENCE | (G,F)-FACTORS | COMPUTER SCIENCE, INFORMATION SYSTEMS | K-FACTORS

Journal Article

Information Processing Letters, ISSN 0020-0190, 2010, Volume 110, Issue 10, pp. 378 - 382

Let G be a graph with vertex set V ( G ) . For any S ⊆ V ( G ) we use ω ( G − S ) to denote the number of components of G − S . The toughness of G, t ( G ) ,...

Fractional [formula omitted]-factor | Combinatorial problems | Toughness | Fractional [formula omitted]-critical graph | Graph | Fractional (g, f)-factor | Fractional (g, f, n)-critical graph | EXISTENCE | COMPUTER SCIENCE, INFORMATION SYSTEMS | Mathematical analysis | Graphs

Fractional [formula omitted]-factor | Combinatorial problems | Toughness | Fractional [formula omitted]-critical graph | Graph | Fractional (g, f)-factor | Fractional (g, f, n)-critical graph | EXISTENCE | COMPUTER SCIENCE, INFORMATION SYSTEMS | Mathematical analysis | Graphs

Journal Article

Information Processing Letters, ISSN 0020-0190, 2011, Volume 111, Issue 9, pp. 403 - 407

Let a , b , k be nonnegative integers with 2 ⩽ a < b and b ⩾ a ( k + 1 ) . An [ a , b ] -factor of a graph G is defined as a spanning subgraph F of G such that...

Combinatorial problems | Toughness | Graph | Minimum degree | [formula omitted]-critical graph | [formula omitted]-factor | [a, b]-factor (a, b,k)-critical graph | EXISTENCE | NUMBER | COMPUTER SCIENCE, INFORMATION SYSTEMS | K-FACTORS | [a, b]-factor | (A,B,K)-CRITICAL GRAPHS | (a, b, k)-critical graph | Integers | Graphs | Images

Combinatorial problems | Toughness | Graph | Minimum degree | [formula omitted]-critical graph | [formula omitted]-factor | [a, b]-factor (a, b,k)-critical graph | EXISTENCE | NUMBER | COMPUTER SCIENCE, INFORMATION SYSTEMS | K-FACTORS | [a, b]-factor | (A,B,K)-CRITICAL GRAPHS | (a, b, k)-critical graph | Integers | Graphs | Images

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2016, Volume 290, pp. 376 - 391

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate...

Critical point theory | Existence and multiplicity | Weighted graph | [formula omitted]Laplacian on a graph | p(·)− Laplacian on a graph | MATHEMATICS, APPLIED | P-LAPLACIAN | GROWTH | EQUATIONS | NEUMANN PROBLEMS | P(.)-LAPLACIAN | p(center dot)-Laplacian on a graph

Critical point theory | Existence and multiplicity | Weighted graph | [formula omitted]Laplacian on a graph | p(·)− Laplacian on a graph | MATHEMATICS, APPLIED | P-LAPLACIAN | GROWTH | EQUATIONS | NEUMANN PROBLEMS | P(.)-LAPLACIAN | p(center dot)-Laplacian on a graph

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 03/2012, Volume 424, pp. 46 - 68

Inheritance is an important and widely spread concept enabling the elegant expression of hierarchy in object-oriented software programs or models. It has been...

Typed attributed graph transformation | Critical pair analysis | [formula omitted]-adhesive category with NACs | Inheritance | M-adhesive category with NACs | SEMANTICS | FORMAL ANALYSIS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | TERMINATION | VERIFICATION

Typed attributed graph transformation | Critical pair analysis | [formula omitted]-adhesive category with NACs | Inheritance | M-adhesive category with NACs | SEMANTICS | FORMAL ANALYSIS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | TERMINATION | VERIFICATION

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2014, Volume 169, pp. 135 - 139

A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the...

Diameter-2-critical | Total domination critical | [formula omitted]-free | Diameter critical

Diameter-2-critical | Total domination critical | [formula omitted]-free | Diameter critical

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2008, Volume 21, Issue 4, pp. 416 - 420

A set D of vertices in a connected graph G is called a k -dominating set if every vertex in G − D is within distance k from some vertex of D . The k...

[formula omitted]-neighborhood | [formula omitted]-distance domination-critical | Diameter | [formula omitted]-domination number | k-neighborhood | k-domination number | k-distance domination-critical | MATHEMATICS, APPLIED | diameter

[formula omitted]-neighborhood | [formula omitted]-distance domination-critical | Diameter | [formula omitted]-domination number | k-neighborhood | k-domination number | k-distance domination-critical | MATHEMATICS, APPLIED | diameter

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2008, Volume 308, Issue 22, pp. 5064 - 5069

A near perfect matching is a matching saturating all but one vertex in a graph. Let G be a connected graph. If any n independent edges in G are contained in a...

Defect [formula omitted]-extendable graph | [formula omitted]-Critical graph | M-alternating path | Near perfect matching | (2 n + 1)-Critical graph | Defect n-extendable graph | (2n+1)-critical graph | MATHEMATICS | defect n-extendable graph | near perfect matching | BIPARTITE GRAPHS

Defect [formula omitted]-extendable graph | [formula omitted]-Critical graph | M-alternating path | Near perfect matching | (2 n + 1)-Critical graph | Defect n-extendable graph | (2n+1)-critical graph | MATHEMATICS | defect n-extendable graph | near perfect matching | BIPARTITE GRAPHS

Journal Article

AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 08/2018, Volume 15, Issue 2, pp. 190 - 196

A k-γ -critical graph is a graph G with connected domination number γ (G)=k and γ (G+uv) Domination | Connected domination | Clique number | critical graphs | Independence number

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2013, Volume 161, Issue 10-11, pp. 1660 - 1668

A vertex subset S of graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S. For a graph G with no isolated vertex, the total...

Total domination | Vertex critical | Diameter | 4-[formula omitted]-critical graph | critical graph

Total domination | Vertex critical | Diameter | 4-[formula omitted]-critical graph | critical graph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2007, Volume 307, Issue 23, pp. 3006 - 3015

A graph G is said to be k- γ -critical if the size of any minimum dominating set of vertices is k, but if any edge is added to G the resulting graph can be...

Domination | Matching | [formula omitted]-Factor-critical | Critical edge | [formula omitted]- [formula omitted]-Critical | Bicritical | Factor-critical | k-γ-Critical | k-Factor-critical | MATHEMATICS | k-gamma-critical | domination | TOUGHNESS | critical edge | factor-critical | bicritical | 3-DOMINATION CRITICAL GRAPHS | matching

Domination | Matching | [formula omitted]-Factor-critical | Critical edge | [formula omitted]- [formula omitted]-Critical | Bicritical | Factor-critical | k-γ-Critical | k-Factor-critical | MATHEMATICS | k-gamma-critical | domination | TOUGHNESS | critical edge | factor-critical | bicritical | 3-DOMINATION CRITICAL GRAPHS | matching

Journal Article

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