Results 61 to 70 of about 332 (184)
The 1 3 $\frac{1}{3}$‐Conjectures for Domination in Cubic Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A set S $S$ of vertices in a graph G $G$ is a dominating set of G $G$ if every vertex not in S $S$ is adjacent to a vertex in S $S$. The domination number of G $G$, denoted by γ ( G ) $\gamma (G)$, is the minimum cardinality among all dominating sets in G $G$. In a breakthrough paper in 2008, Löwenstein and Rautenbach proved that if G $G$ is a
Paul Dorbec, Michael A. Henning
wiley +1 more source
Forbidden Subgraphs and Complete Partitions
The Electronic Journal of CombinatoricsA graph is called an $(r,k)$-graph if its vertex set can be partitioned into $r$ parts, each having at most $k$ vertices and there is at least one edge between any two parts. Let $f(r,H)$ be the minimum $k$ for which there exists an $H$-free $(r,k)$-graph.
John Byrne, Michael Tait, Craig Timmons
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Forbidden subgraphs and the Kőnig property
Electronic Notes in Discrete Mathematics, 2011 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 ...
Mitre Costa Dourado +4 more
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The Minimal Nonplanar Strong Digraphs
Journal of Graph Theory, EarlyView.ABSTRACT Kuratowski's theorem says that the minimal (under subgraph containment) graphs that are not planar are the subdivisions of K 5 ${K}_{5}$ and of K 3 , 3 ${K}_{3,3}$. Here we study the minimal (under subdigraph containment) strongly‐connected digraphs that are not planar.
Stephen Bartell, Paul Seymour
wiley +1 more source
Theory and Applications of GraphsA class G of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by G^{apex} the class of graphs G that contain a vertex v such that G − v is in G.
Jagdeep Singh +2 more
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Some Variations of Perfect Graphs
Discussiones Mathematicae Graph Theory, 2016 We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively.
Dettlaff Magda +3 more
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A Structural Description of Zykov and Blanche Descartes Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Around 1950, Zykov and Blanche Descartes proposed the two first explicit constructions of triangle‐free graphs with arbitrarily large chromatic number. We define a Zykov (resp. Blanche Descartes) graph as any induced subgraph of a graph created using Zykov's construction (resp. Blanche Descartes's).
Malory Marin +3 more
wiley +1 more source
On Graphs with Chromatic Number and Maximum Degree Both Equal to Nine
Theory and Applications of GraphsAn equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with $\chi = \Delta = 9$ contains $K_3 \lor E_6$ as a subgraph.
Rachel Galindo, Jessica McDonald
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Heuristic approaches for a new variant of the team orienteering problem
International Transactions in Operational Research, Volume 34, Issue 2, Page 975-1002, March 2027.Abstract In this paper, we tackle the team orienteering problem (TOP) with service times, mandatory nodes and incompatibilities arising from two real‐world healthcare applications. We propose two heuristic algorithms: a variable neighbourhood descent algorithm and a matheuristic based on a cut separation approach.
Alberto Guastalla +2 more
wiley +1 more source
Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}.
Crane Charles Brian
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