Results 31 to 40 of about 735 (221)

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
openaire   +3 more sources

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Complexity Framework for Forbidden Subgraphs I: The Framework [PDF]

Algorithmica
Abstract For a set of graphs $${\mathcal {H}}$$ H , a graph G is $${\mathcal {H}}$$ H -subgraph-free if G does not contain
Matthew Johnson, Barnaby Martin, Jelle J. Oostveen, Sukanya Pandey, Daniël Paulusma, Siani Smith, Erik Jan van Leeuwen   +6 more
openalex   +3 more sources

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, Broersma Hajo, Zhang Shenggui   +2 more
doaj   +1 more source

A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2

Algorithms, 2021
Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of
Serafino Cicerone
doaj   +1 more source