Results 41 to 50 of about 9,740 (155)
AKCE International Journal of Graphs and Combinatorics, 2017 The extremal number or simply denotes the maximal number of edges in a graph on vertices with forbidden subgraphs and . The exact number of is only known for up to and . There are upper and lower bounds of for other values of .
Novi H. Bong
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On bounding the difference between the maximum degree and the chromatic number by a constant
, 2016 We provide a finite forbidden induced subgraph characterization for the graph class $\varUpsilon_k$, for all $k \in \mathbb{N}_0$, which is defined as follows.
Schaudt, Oliver, Weil, Vera
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Electronic Notes in Discrete Mathematics, 2017 In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other popular orderings and leads to different basic questions.
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On Critical Unicyclic Graphs with Cutwidth Four
AppliedMath, 2022 The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line Pn with n=|V(G)| vertices in such a way that the maximum number of overlapping edges (i.e., the congestion) is minimized.
Zhenkun Zhang, Hongjian Lai
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Forbidden subgraphs that imply hamiltonian‐connectedness* [PDF]
Journal of Graph Theory, 2002 AbstractIt is proven that if G is a 3‐connected claw‐free graph which is also H1‐free (where H1 consists of two disjoint triangles connected by an edge), then G is hamiltonian‐connected. Also, examples will be described that determine a finite family of graphs ${\cal L}$ such that if a 3‐connected graph being claw‐free and L‐free implies G is ...
Hajo Broersma +4 more
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Heavy subgraph pairs for traceability of block-chains
Discussiones Mathematicae Graph Theory, 2014 A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type ...
Li Binlong +2 more
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On the chromatic number of (P_{5},windmill)-free graphs [PDF]
Opuscula Mathematica, 2017 In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint ...
Ingo Schiermeyer
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Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
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Coloring Graphs Characterized by a Forbidden Subgraph [PDF]
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Petr A. Golovach +2 more
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On Sequential Heuristic Methods for the Maximum Independent Set Problem
Discussiones Mathematicae Graph Theory, 2017 We consider sequential heuristics methods for the Maximum Independent Set (MIS) problem. Three classical algorithms, VO [11], MIN [12], or MAX [6] , are revisited. We combine Algorithm MIN with the α-redundant vertex technique[3].
Lê Ngoc C. +2 more
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