Discrete Applied Mathematics, ISSN 0166-218X, 02/2018, Volume 236, pp. 422 - 427

We discuss some problems related to induced subgraphs. (1)A good upper bound for the chromatic number in terms of the clique number for graphs in which every...

Forbidden induced subgraph | Clique number | Chromatic number | Induced subgraph | Perfect graph | NP-completeness | MATHEMATICS, APPLIED | HOLES | FREE GRAPHS | Mathematics - Combinatorics

Forbidden induced subgraph | Clique number | Chromatic number | Induced subgraph | Perfect graph | NP-completeness | MATHEMATICS, APPLIED | HOLES | FREE GRAPHS | Mathematics - Combinatorics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 12/2017, Volume 340, Issue 12, pp. 2878 - 2888

We call a graph Gpancyclic if it contains at least one cycle of every possible length m, for 3≤m≤|V(G)|. In this paper, we define a new property called chorded...

Forbidden subgraph | Chorded cycle | Hamiltonian | Pancyclic | MATHEMATICS | HAMILTONIAN PROPERTIES | Mathematics - Combinatorics

Forbidden subgraph | Chorded cycle | Hamiltonian | Pancyclic | MATHEMATICS | HAMILTONIAN PROPERTIES | Mathematics - Combinatorics

Journal Article

Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 02/2018, Volume 89

Conference Proceeding

Discrete Mathematics, ISSN 0012-365X, 10/2015, Volume 338, Issue 10, pp. 1706 - 1713

A connected edge-colored graph G is rainbow-connected if any two distinct vertices of G are connected by a path whose edges have pairwise distinct colors; the...

Rainbow connection | Forbidden subgraph | Edge coloring | MATHEMATICS | NUMBER | DIAMETER | MINIMUM DEGREE | GRAPHS

Rainbow connection | Forbidden subgraph | Edge coloring | MATHEMATICS | NUMBER | DIAMETER | MINIMUM DEGREE | GRAPHS

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 07/2017, Volume 33, Issue 4, pp. 999 - 1008

A tree in an edge-colored connected graph G is called a rainbow tree if no two edges of it are assigned the same color. For a vertex subset , a tree is called...

Forbidden subgraphs | k-rainbow index | 3-rainbow index | Rainbow tree | MATHEMATICS | RAINBOW CONNECTION

Forbidden subgraphs | k-rainbow index | 3-rainbow index | Rainbow tree | MATHEMATICS | RAINBOW CONNECTION

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2015, Volume 29, Issue 1, pp. 65 - 78

We study two extremal problems about subgraphs excluding a family F of graphs: (i) Among all graphs with m edges, what is the smallest size f(m, F) of a...

Forbidden subgraphs | Probabilistic methods | Degrees | Girth | Spanning subgraphs | MATHEMATICS, APPLIED | forbidden subgraphs | girth | probabilistic methods | spanning subgraphs | degrees | BIPARTITE GRAPHS | Mathematics - Combinatorics | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Graph theory | Grafs, Teoria de | Àrees temàtiques de la UPC

Forbidden subgraphs | Probabilistic methods | Degrees | Girth | Spanning subgraphs | MATHEMATICS, APPLIED | forbidden subgraphs | girth | probabilistic methods | spanning subgraphs | degrees | BIPARTITE GRAPHS | Mathematics - Combinatorics | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Graph theory | Grafs, Teoria de | Àrees temàtiques de la UPC

Journal Article

Discrete Mathematics, ISSN 0012-365X, 12/2017, Volume 340, Issue 12, pp. 2792 - 2797

Let H={H1,…,Hk} be a set of connected graphs. A graph is said to be H-free if it does not contain any member of H as an induced subgraph. We show that if the...

Supereulerian | Claw-free | Forbidden set | Induced subgraph | MATHEMATICS | TRIPLES | TRACEABILITY | PAIRS

Supereulerian | Claw-free | Forbidden set | Induced subgraph | MATHEMATICS | TRIPLES | TRACEABILITY | PAIRS

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 11/2018, Volume 34, Issue 6, pp. 1671 - 1690

A graph is called H-free if it has no induced subgraph isomorphic to H. A graph is called N-i-locally connected if G[{x is an element of V(G) : 1 <= d(G)(w, x)...

Forbidden subgraph | Collapsible | Supereulerian | 2-factor | Hamiltonian | CLAW | MATHEMATICS | SUPEREULERIAN GRAPHS | PAIRS | Algorithms | Apexes | Traveling salesman problem | Graph theory

Forbidden subgraph | Collapsible | Supereulerian | 2-factor | Hamiltonian | CLAW | MATHEMATICS | SUPEREULERIAN GRAPHS | PAIRS | Algorithms | Apexes | Traveling salesman problem | Graph theory

Journal Article

Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 08/2018, Volume 116

Conference Proceeding

Discrete Mathematics, ISSN 0012-365X, 06/2019, Volume 342, Issue 6, pp. 1602 - 1608

Considering connected K1,3-free graphs with independence number at least 3, Chudnovsky and Seymour (2010) showed that every such graph, say G, is 2ω-colourable...

Vertex colouring | Forbidden induced subgraphs | Perfect graphs

Vertex colouring | Forbidden induced subgraphs | Perfect graphs

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2016, Volume 339, Issue 2, pp. 533 - 538

A graph G has p-intersection number at most d if it is possible to assign to every vertex u of G, a subset S(u) of some ground set U with |U|=d in such a way...

Forbidden induced subgraph | [formula omitted]-intersection number | Intersection number | Intersection graph | p-intersection number | MATHEMATICS | DOT PRODUCT REPRESENTATIONS | GRAPHS

Forbidden induced subgraph | [formula omitted]-intersection number | Intersection number | Intersection graph | p-intersection number | MATHEMATICS | DOT PRODUCT REPRESENTATIONS | GRAPHS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2017, Volume 37, Issue 3, pp. 691 - 710

Let be a graph. Adopting the terminology of Broersma and Čada, respectively, we say that is 2-heavy if every induced claw ( ) of contains two end-vertices each...

closure theory | 05C45 | 05C38 | heavy subgraphs | hamiltonian graphs | Hamiltonian graphs | Heavy subgraphs | Closure theory | MATHEMATICS | CYCLES | CLOSURE | CLAW-FREE GRAPHS | FORBIDDEN SUBGRAPHS | Mathematics - Combinatorics

closure theory | 05C45 | 05C38 | heavy subgraphs | hamiltonian graphs | Hamiltonian graphs | Heavy subgraphs | Closure theory | MATHEMATICS | CYCLES | CLOSURE | CLAW-FREE GRAPHS | FORBIDDEN SUBGRAPHS | Mathematics - Combinatorics

Journal Article

GRAPHS AND COMBINATORICS, ISSN 0911-0119, 01/2019, Volume 35, Issue 1, pp. 1 - 31

A graph G with clique number (G) and chromatic number (G) is perfect if (H)=(H) for every induced subgraph H of G. A family G of graphs is called -bounded with...

Forbidden induced subgraph | HOLE | Perfect graphs | Chromatic number | bounded | binding function | MATHEMATICS | TREES | 3-COLORABILITY | BOUNDS | P-5 | FREE GRAPHS | EVEN

Forbidden induced subgraph | HOLE | Perfect graphs | Chromatic number | bounded | binding function | MATHEMATICS | TREES | 3-COLORABILITY | BOUNDS | P-5 | FREE GRAPHS | EVEN

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 11/2013, Volume 161, Issue 16-17, pp. 2380 - 2388

The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet...

Forbidden subgraphs | Maximum matching | Edge-perfect graphs | König–Egerváry property | König–Egerváry graphs | König-Egerváry property | König-Egerváry graphs | MATHEMATICS, APPLIED | NUMBER | Konig-Egervary property | MAXIMUM MATCHINGS | THEOREM | GAMES | GREEDOIDS | Konig-Egervary graphs | GRAPHS

Forbidden subgraphs | Maximum matching | Edge-perfect graphs | König–Egerváry property | König–Egerváry graphs | König-Egerváry property | König-Egerváry graphs | MATHEMATICS, APPLIED | NUMBER | Konig-Egervary property | MAXIMUM MATCHINGS | THEOREM | GAMES | GREEDOIDS | Konig-Egervary graphs | GRAPHS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 02/2020, Volume 40, Issue 1, pp. 195 - 208

A graph is if the neighbourhood ) induces a connected subgraph for each vertex in . For a graph , the of is the number of vertices unsaturated by a maximum...

05C70 | 05C40 | CLAW | MATHEMATICS | deficiency | locally-connected graph | BOUNDS | forbidden subgraph | matching | 05c70 | 05c40

05C70 | 05C40 | CLAW | MATHEMATICS | deficiency | locally-connected graph | BOUNDS | forbidden subgraph | matching | 05c70 | 05c40

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 02/2014, Volume 522, pp. 34 - 43

A colouring of a graph G=(V,E) is a mapping c:V→{1,2,…} such that c(u)≠c(v) if uv∈E; if |c(V)|⩽k then c is a k-colouring. The Colouring problem is that of...

Independent set | Clique | Colouring | Forbidden induced subgraphs | BOUNDED CLIQUE-WIDTH | K-COLORABILITY | COMPUTER SCIENCE, THEORY & METHODS | TRIANGLE-FREE GRAPHS

Independent set | Clique | Colouring | Forbidden induced subgraphs | BOUNDED CLIQUE-WIDTH | K-COLORABILITY | COMPUTER SCIENCE, THEORY & METHODS | TRIANGLE-FREE GRAPHS

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 331 - 363

For a positive integer k, a k‐coloring of a graph G=(V,E) is a mapping c:V→{1,2,...,k} such that c(u)≠c(v) whenever uv∈E. The Coloring problem is to decide,...

precoloring extension | graph coloring | forbidden induced subgraph | list coloring | choosability | CHROMATIC NUMBER | CLAW-FREE GRAPHS | TRIANGLE-FREE GRAPHS | NP-COMPLETENESS | MATHEMATICS | UPPER-BOUNDS | 3-COLORABILITY | K-COLORABILITY | ABSENCE | VERTICES | INDEX

precoloring extension | graph coloring | forbidden induced subgraph | list coloring | choosability | CHROMATIC NUMBER | CLAW-FREE GRAPHS | TRIANGLE-FREE GRAPHS | NP-COMPLETENESS | MATHEMATICS | UPPER-BOUNDS | 3-COLORABILITY | K-COLORABILITY | ABSENCE | VERTICES | INDEX

Journal Article

GRAPHS AND COMBINATORICS, ISSN 0911-0119, 07/2017, Volume 33, Issue 4, pp. 969 - 979

We consider the connected graphs G that satisfy the following property: If are integers, then any coloring of the edges of , using m colors, containing no...

MATHEMATICS | Forbidden Subgraph | 6-Cycle | Monochromatic Connectivity | Edge-Coloring

MATHEMATICS | Forbidden Subgraph | 6-Cycle | Monochromatic Connectivity | Edge-Coloring

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2019, Volume 342, Issue 3, pp. 635 - 642

The chromatic number of a graph is the minimum k such that the graph has a proper k-coloring. There are many coloring parameters in the literature that are...

Star coloring | Forbidden characterization | Chromatic number | Acyclic coloring | MATHEMATICS | TREES | GRAPHS | Mathematics - Combinatorics

Star coloring | Forbidden characterization | Chromatic number | Acyclic coloring | MATHEMATICS | TREES | GRAPHS | Mathematics - Combinatorics

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 01/2019, Volume 90, Issue 1, pp. 61 - 82

Let H be a set of connected graphs, each of which has order at least three, and suppose that there exist infinitely many connected H‐free graphs of minimum...

forbidden subgraph | 2‐factor | 2-factor | FINITE-SET | MATHEMATICS | HAMILTONIAN PROPERTIES | FREE GRAPHS

forbidden subgraph | 2‐factor | 2-factor | FINITE-SET | MATHEMATICS | HAMILTONIAN PROPERTIES | FREE GRAPHS

Journal Article

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