Results 31 to 40 of about 332 (184)
Vertex Colouring and Forbidden Subgraphs ? A Survey [PDF]
Graphs and Combinatorics, 2004 The monograph ``Graph coloring problems'' by \textit{T. R. Jensen} and \textit{B. Toft} (Wiley, New York) (1995; Zbl 0855.05054) provides a comprehensive list of unsolved problems in chromatic graph theory. The present survey gives an account of the recent development in the area.
Randerath, Bert, Schiermeyer, Ingo
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Theory and Applications of GraphsFor a family $\mathcal{H}$ of graphs, a graph $G$ is said to be $\mathcal{H}$-free if $G$ contains no member of $\mathcal{H}$ as an induced subgraph. Let $\mathcal{G}_2^{(3)}}(\mathcal{H})$ denote the family of $2$-connected $\mathcal{H}$-free graphs ...
Takafumi Kotani, Yoshimi Egawa
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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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Deficiency and Forbidden Subgraphs of Connected, Locally-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 A graph G is locally-connected if the neighbourhood NG(v) induces a connected subgraph for each vertex v in G. For a graph G, the deficiency of G is the number of vertices unsaturated by a maximum matching, denoted by def(G). In fact, the deficiency of a
Li Xihe, Wang Ligong
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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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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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Some Characterizations and NP-Complete Problems for Power Cordial Graphs
Journal of Mathematics, 2023 A power cordial labeling of a graph G=VG,EG is a bijection f:VG⟶1,2,…,VG such that an edge e=uv is assigned the label 1 if fu=fvn or fv=fun, for some n∈N∪0 and the label 0 otherwise, and satisfy the number of edges labeled with 0 and the number of edges ...
C. M. Barasara, Y. B. Thakkar
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Forbidden subgraphs in the norm graph
Discrete Mathematics, 2016 We show that the norm graph constructed in [J. Kollár, L. Rónyai and T. Szabó, Norm-graphs and bipartite Turán numbers, Combinatorica, 16 (1996) 399--406] with $n$ vertices about $\frac{1}{2}n^{2-1/t}$ edges, which contains no copy of $K_{t,(t-1)!+1}$, does not contain a copy of $K_{t+1,(t-1)!-1}$.
Ball, Simeon, PEPE, VALENTINA
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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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Line Graphs of Multigraphs and the Forbidden Graph E 6
Journal of Graph Theory, EarlyView.ABSTRACT The line graph Γ of a multigraph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of the 32 graphs, all of which
Hans Cuypers
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