101–114 of
114 results.

Clive Elphick
•
Pawel Wocjan
In this paper, we define and compare three new measures of graph irregularity. We use these measures to tighten upper bounds for the chromatic number and the Colin de Verdiere parameter. We also stren...

Yanbo Zhang
•
Hajo Broersma
•
Yaojun Chen
Given two graphs G1 and G2, the Ramsey number R(G1;G2)is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn ...

Maria Timkova
The Hforce number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with W = k such that each cycle passing through all vertices of W is a hamilt...

Peter Burcsi
•
Daniel T. Nagy
For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $\mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many...

Michalis Christou
•
Costas Iliopoulos
•
Mirka Miller
The Ramsey number R(m, n) is the smallest integer p such that any bluered colouring of the edges of the complete graph Kp forces the appearance of a blue Km or a red Kn. Bipartite Ramsey problems dea...

Jemal Abawajy
•
Andrei Kelarev
•
Morshed Chowdhury
This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also inclu...

Martin Baca
•
Ljiljana Brankovic
•
Marcela Lascsakova
•
Oudone Phanalasy
•
Andrea SemanicovaFenovciova
The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A la...

Francesc Comellas
•
Cristina Dalfo
•
Miquel Àngel Fiol
We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can...

Binlong Li
•
Hajo Broersma
•
Shenggui Zhang
A blockchain is a graph whose block graph is a path, i.e. it is either a $P_1$, a $P_2$, or a 2connected graph, or a graph of connectivity 1 with exactly two endblocks. A graph is called traceable ...

Edy Tri Baskoro
•
A. Asmiati
Let $c$ be a proper $k$coloring of a connected graph $G$. Let $\Pi = \{S_{1}, S_{2},\ldots, S_{k}\}$ be the induced partition of $V(G)$ by $c$, where $S_{i}$ is the partition class having all vert...

Ayesha Shabbir
•
Carol T. Zamfirescu
•
Tudor I. Zamfirescu
This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher ...

Charles Delorme
Given a subset C in a metric space E, its successor is the subset s(C) of points at maximum distance from C in E. We study some properties of the sequence obtained by iterating this operation. Graph...

Hongliang Lu
•
Yuqing Lin
In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edgeconnectivity. Moreover, we also show that our condition is sharp.

Ali Ahmad
•
Martin Baca
•
Muhammad Numan
We investigate the vertex total and edge total modication of the wellknown irregularity strength of graphs. We have determined the exact values of the total vertex irregularity strength and the total...