Results 31 to 40 of about 69,865 (208)

Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs

Discussiones Mathematicae Graph Theory, 2022
A graph G is called Hamilton-connected if for every pair of distinct vertices {u, v} of G there exists a Hamilton path in G that connects u and v. A graph G is said to be t-tough if t·ω(G − X) ≤ |X| for all X ⊆ V (G) with ω(G − X) > 1. The toughness of G,
Zheng Wei, Broersma Hajo, Wang Ligong
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Stars in forbidden triples generating a finite set of graphs with minimum degree four

Electronic Journal of Graph Theory and Applications
For a family H of graphs, a graph G is said to be H-free if G contains no member of H as a induced subgraph. Let G4(H) denote the family of connected H-free graphs having minimum degree at least 4.
Takafumi Kotani
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Weakly threshold graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2018
We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$.
Michael D. Barrus
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Forbidden subgraphs, stability and hamiltonicity

Discrete Mathematics, 1999
The authors study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in \textit{Z. Ryjáček} [J. Comb. Theory, Ser. B 70, No.~2, 217-224 (1997; Zbl 0872.05032)]. They characterize all connected graphs \(A\) such that the class of all \(CA\)-free graphs (where \(C\) denotes the ...
Jan Brousek, Zdenek Ryjácek, Ingo Schiermeyer   +2 more
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3-Rainbow Index and Forbidden Subgraphs [PDF]

Graphs and Combinatorics, 2017
11 ...
Wenjing Li, Xueliang Li 0001, Jingshu Zhang   +2 more
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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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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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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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Forbidden triples for $2$-connected graphs with minimum degree three which contain $K_4$ and $K_{2,2}$

Theory and Applications of Graphs
For 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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Some new upper bounds of

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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