Results 51 to 60 of about 10,864 (212)

On Critical Unicyclic Graphs with Cutwidth Four

open access: yesAppliedMath, 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

Heavy subgraph pairs for traceability of block-chains

open access: yesDiscussiones 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
doaj   +1 more source

On the chromatic number of (P_{5},windmill)-free graphs [PDF]

open access: yesOpuscula 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

On coloring digraphs with forbidden induced subgraphs

open access: yesJournal of Graph Theory, 2022
AbstractWe prove a conjecture by Aboulker, Charbit, and Naserasr by showing that every oriented graph in which the out‐neighborhood of every vertex induces a transitive tournament can be partitioned into two acyclic induced subdigraphs. We prove multiple extensions of this result to larger classes of digraphs defined by a finite list of forbidden ...
openaire   +3 more sources

Colouring graphs with forbidden bipartite subgraphs

open access: yesCombinatorics, Probability and Computing, 2022
AbstractA conjecture of Alon, Krivelevich and Sudakov states that, for any graph $F$ , there is a constant $c_F \gt 0$ such that if $G$ is an $F$ -free graph of maximum degree $\Delta$ , then $\chi\!(G) \leqslant c_F \Delta/ \log\!\Delta$ . Alon, Krivelevich and Sudakov verified this conjecture for a class of graphs $F$ that includes all ...
James Anderson   +2 more
openaire   +2 more sources

New results on connected dominating structures in graphs

open access: yesActa Universitatis Sapientiae: Informatica, 2019
A set of vertices in a graph is a dominating set if every vertex not in the set is adjacent to at least one vertex in the set. A dominating structure is a subgraph induced by the dominating set.
Samuel Libin Chacko, Joseph Mayamma
doaj   +1 more source

Problems in extremal graph theory [PDF]

open access: yes, 2010
We consider a variety of problems in extremal graph and set theory. The {\em chromatic number} of $G$, $\chi(G)$, is the smallest integer $k$ such that $G$ is $k$-colorable.
Ozkahya, Lale
core  

On bounding the difference between the maximum degree and the chromatic number by a constant

open access: yes, 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
core   +1 more source

Graphs with small diameter determined by their $D$-spectra [PDF]

open access: yes, 2018
Let $G$ be a connected graph with vertex set $V(G)=\{v_{1},v_{2},...,v_{n}\}$. The distance matrix $D(G)=(d_{ij})_{n\times n}$ is the matrix indexed by the vertices of $G,$ where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j ...
Liu, Ruifang, Xue, Jie
core   +2 more sources

On Sequential Heuristic Methods for the Maximum Independent Set Problem

open access: yesDiscussiones 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
doaj   +1 more source

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