Results 81 to 90 of about 10,864 (212)
Small clique number graphs with three trivial critical ideals [PDF]
The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals.
Carlos, Carlos A. Alfaro, E. Valencia
core
Largest chordal and interval subgraphs faster than 2^n
We prove that in an n-vertex graph, induced chordal and interval subgraphs with the maximum number of vertices can be found in time $O(2^{\lambda n})$ for some ...
Bliznets, Ivan+3 more
core +1 more source
Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis.
A. Cournier+17 more
core +1 more source
Forbidden subgraphs that imply 2-factors
AbstractThe connected forbidden subgraphs and pairs of connected forbidden subgraphs that imply a 2-connected graph is hamiltonian have been characterized by Bedrossian [Forbidden subgraph and minimum degree conditions for hamiltonicity, Ph.D. Thesis, Memphis State University, 1991], and extensions of these excluding graphs for general graphs of order ...
Ralph J. Faudree+2 more
openaire +2 more sources
Heavy subgraphs, stability and hamiltonicity
Let $G$ be a graph. Adopting the terminology of Broersma et al. and \v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every
Li, Binlong, Ning, Bo
core +2 more sources
Traceability in graphs with forbidden triples of subgraphs
AbstractIf 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. In a previous paper (Gould and Harris, 1995) the authors demonstrated two families of triples of subgraphs which imply traceability ...
John M. Harris, Ronald J. Gould
openaire +2 more sources
On bounding the difference of the maximum degree and clique number [PDF]
For every k ∈ ℕ0, we consider graphs in which for any induced subgraph, Δ ≤ ω−1+k holds, where Δ is the maximum degree and ω is the maximum clique number of the subgraph. We give a finite forbidden induced subgraph characterization for every k.
Schaudt, Oliver, Weil, Vera
core
Rainbow connection and forbidden subgraphs
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 number rc ( G ) of G is the minimum number of colors such that G is rainbow-connected.
Ingo Schiermeyer+3 more
openaire +2 more sources
Forbidden subgraphs for constant domination number
In this paper, we characterize the sets $\mathcal{H}$ of connected graphs such that there exists a constant $c=c(\mathcal{H})$ satisfying $\gamma (G)\leq c$ for every connected $\mathcal{H}$-free graph $G$, where $\gamma (G)$ is the domination number of $G$.Comment: 6 pages, 1 ...
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Forbidden subgraphs and the Kőnig property
Abstract A graph has the Kőnig property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Kőnig property by forbidden subgraphs, restricted to graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszʼs result to a characterization of all graphs having the Kőnig ...
Luerbio Faria+10 more
openaire +2 more sources