Results 51 to 60 of about 332 (184)

Characterizing the forbidden pairs for graphs to be super-edge-connected

AKCE International Journal of Graphs and Combinatorics
Let [Formula: see text] be a set of given connected graphs. A graph G is said to be [Formula: see text]-free if G contains no H as an induced subgraph for any [Formula: see text].
Hazhe Ye, Yingzhi Tian
doaj   +1 more source

On the 12-Representability of Induced Subgraphs of a Grid Graph

Discussiones Mathematicae Graph Theory, 2022
The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
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

Ramsey-type Theorems with Forbidden Subgraphs [PDF]

Combinatorica, 2001
P. Erdős and A. Hajnal conjectured that for every finite graph \(H\) every \(H\)-free graph on \(n\) vertices contains a complete or empty subgraph of size \(n^{\varepsilon(H)}\). It is shown that if the conjecture holds for \(H_1\), \(H_2\) then it holds for the graph which is \(H_1\) with one vertex blown up to a copy of \(H_2\).
Alon, Noga, Pach, János, Solymosi, József   +2 more
openaire   +2 more sources

A Note on Lovász Characterization of Perfect Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A graph is perfect if, for every induced subgraph, the chromatic number equals the size of its largest clique. In 1972, Lovász established a fundamental characterization of perfect graphs, showing that a graph is perfect if and only if, for every induced subgraph, the product of the size of the largest independent set and the size of the ...
James Alex
wiley   +1 more source

Forbidden subgraphs for supereulerian and hamiltonian graphs

Discrete Applied Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaojing Yang, Junfeng Du, Liming Xiong
openaire   +3 more sources

Characterization of Graphs Without Even F $F$‐Orientations

Journal of Graph Theory, EarlyView.
ABSTRACT A graph G $G$ is 1‐extendable if every edge belongs to at least one 1‐factor of G $G$. Let G $G$ be a graph with a 1‐factor F $F$. Then an even (odd) F $F$ ‐orientation of G $G$ is an orientation in which each F $F$‐alternating cycle has exactly an even (odd) number of edges directed in the same fixed direction around the cycle.
Marién Abreu, Domenico Labbate, Federico Romaniello, John Sheehan   +3 more
wiley   +1 more source

Graphs whose Laplacian eigenvalues are almost all 1 or 2

Special Matrices
We explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
doaj   +1 more source

The Largest Subgraph Without A Forbidden Induced Subgraph

Combinatorica
20 ...
Fox, Jacob, Nenadov, Rajko, Pham, Huy Tuan   +2 more
openaire   +3 more sources

On Graphs Which Have Locally Complete 2‐Edge‐colourings and Their Relationship to Proper Circular‐Arc Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A 2‐edge‐coloured graph G $G$ is called locally complete if for each vertex v $v$, the vertices adjacent to v $v$ through edges of the same colour induce a complete subgraph in G $G$. Locally complete 2‐edge‐coloured graphs have nice properties, and there exists a polynomial algorithm to decide whether such a graph has an alternating ...
Jørgen Bang‐Jensen, Jing Huang
wiley   +1 more source