Results 21 to 30 of about 38,756 (312)

The Windy Postman Problem on Series-Parallel Graphs [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2005
The windy postman problem is the NP-hard problem of finding the minimum cost of a tour traversing all edges of an undirected graph, where the cost of traversal of an edge depends on the direction. Given an undirected graph $G$, we consider the polyhedron
Francisco Javier Zaragoza Martínez
doaj   +1 more source

On very strongly perfect Cartesian product graphs

open access: yesAIMS Mathematics, 2022
Let $ G_1 \square G_2 $ be the Cartesian product of simple, connected and finite graphs $ G_1 $ and $ G_2 $. We give necessary and sufficient conditions for the Cartesian product of graphs to be very strongly perfect.
Ganesh Gandal   +2 more
doaj   +1 more source

Defective Coloring on Classes of Perfect Graphs [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2022
In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$.
Rémy Belmonte   +2 more
doaj   +1 more source

Characterising and recognising game-perfect graphs [PDF]

open access: yesDiscrete Mathematics & Theoretical Computer Science, 2019
Consider a vertex colouring game played on a simple graph with $k$ permissible colours. Two players, a maker and a breaker, take turns to colour an uncoloured vertex such that adjacent vertices receive different colours.
Dominique Andres, Edwin Lock
doaj   +1 more source

Sum-perfect graphs [PDF]

open access: yesDiscrete Applied Mathematics, 2019
Inspired by a famous characterization of perfect graphs due to Lov sz, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $ (H) + (H) \geq |V(H)|$. (Here $ $ and $ $ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $
Bart Litjens   +2 more
openaire   +2 more sources

Some Variations of Perfect Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2016
We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively.
Dettlaff Magda   +3 more
doaj   +1 more source

Nearly perfect sets in the n-fold products of graphs [PDF]

open access: yesOpuscula Mathematica, 2007
The study of nearly perfect sets in graphs was initiated in [J. E. Dunbar, F. C. Harris, S. M. Hedetniemi, S. T. Hedetniemi, A. A. McRae, R. C. Laskar, Nearly perfect sets in graphs, Discrete Mathematics 138 (1995), 229-246]. Let \(S \subseteq V(G)\). We
Monika Perl
doaj  

Perfect edge domination in vague graphs

open access: yesRatio Mathematica, 2021
In this paper, we modified undirected vague graphs and edge domination set based on these two concepts. We study the notions of perfect edge domination, connected perfect edge domination of vague graph. Moreover, we investigate some related properties in
M Kaliraja, P Kanibose, Abdul Ibrahim
doaj   +1 more source

Perfect codes in power graphs of finite groups

open access: yesOpen Mathematics, 2017
The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong   +4 more
doaj   +1 more source

Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

open access: yesDiscussiones Mathematicae Graph Theory, 2017
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers.
Borowiecka-Olszewska Marta   +1 more
doaj   +1 more source

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