Results 21 to 30 of about 38,756 (312)
The Windy Postman Problem on Series-Parallel Graphs [PDF]
Discrete 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
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On very strongly perfect Cartesian product graphs
AIMS 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
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Defective Coloring on Classes of Perfect Graphs [PDF]
Discrete 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
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Characterising and recognising game-perfect graphs [PDF]
Discrete 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
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Discrete 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
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Some Variations of Perfect Graphs
Discussiones 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
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Nearly perfect sets in the n-fold products of graphs [PDF]
Opuscula 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
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Perfect edge domination in vague graphs
Ratio 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
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Perfect codes in power graphs of finite groups
Open 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
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Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
Discussiones 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
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