Results 91 to 100 of about 566 (185)
List coloring ordered graphs with forbidden induced subgraphs
CoRRIn the List $k$-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of $\{1,\ldots,k\}$. We need to decide if $G$ admits a proper coloring, where every vertex receives a color from its list. The complexity of the problem in classes defined by forbidding induced subgraphs is a widely studied topic in ...
Piecyk, Marta, Rzążewski, Paweł
openaire +3 more sources
A note on an induced subgraph characterization of domination perfect graphs
, 2017 Let γ(G) and ι(G) be the domination and independent domina- tion numbers of a graph G, respectively. Introduced by Sumner and Moorer [23], a graph G is domination perfect if γ(H) = ι(H) for every induced subgraph H ⊆ G.
Plein, Fränk, Camby, Eglantine
core +1 more source
, 2004 The direct sum of a finite number of graph classes H_1, ..., H_k is defined as the set of all graphs formed by taking the union of graphs from each of the H_i. The join of these graph classes is similarly defined as the set of all graphs formed by taking
Barrus, Michael D.
core
Traceability in graphs with forbidden triples of subgraphs
, 1998 If F is a collection of connected graphs, and if a graph G does not contain any member of F as an induced subgraph, then G is said to be F-free. The members of F in this situation are called forbidden subgraphs.
Ronald J. Gould +3 more
core +1 more source
Hadwiger’s Conjecture with Certain Forbidden Induced Subgraphs
Experimental MathematicsWe prove that $\{\overline{K_3}, H\}$-free graphs are not counterexamples to Hadwiger's Conjecture, where $H$ is any one of 33 graphs on seven, eight, or nine vertices, or $H=K_8$. This improves on past results of Plummer-Stiebitz-Toft, Kriesell, and Bosse. The proofs are mostly computer-assisted.
openaire +2 more sources
Minimal forbidden subgraphs of reducible graph properties
, 2001 A property of graphs is any class of graphs closed under isomorphism. Let ₁,₂,...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable if the vertex set V(G) can be partitioned into n sets, {V₁,V₂,..., Vₙ}, such that for each i = 1,2,...,n ...
Berger, Amelie
core +1 more source
On forbidden induced subgraphs for K_{1,3}-free perfect graphs
Discret. Math., 2019 Considering connected $K_{1,3}$-free graphs with independence number at least $3$, Chudnovsky and Seymour (2010) showed that every such graph, say $G$, is $2ω$-colourable where $ω$ denotes the clique number of $G$. We study $(K_{1,3}, Y)$-free graphs, and show that the following three statements are equivalent.
Brause, Christoph +5 more
openaire +5 more sources
Forbidden induced subgraphs for threshold-like graph classes
, 2019 Every hereditary graph class (closed under induced subgraphs) has a characterization by forbidden induced subgraphs: graphs not in the class but every graph obtained by deleting a vertex is in the class.
Sivaraman, Vaidyanathan
core
, 2014 In this paper, we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph. We look at node deletion problems for non-trivial properties which can be characterized by forbidden structure which
Kumar, Mrinal +3 more
core +1 more source
Coloring Algorithms for Graphs and Hypergraphs with Forbidden Substructures [PDF]
, 2022 This thesis mainly focus on complexity results of the generalized version of the $r$-Coloring Problem, the $r$-Pre-Coloring Extension Problem and the List $r$-Coloring Problem restricted to hypergraphs and ordered graphs with forbidden substructures ...
Li, Yanjia
core