Results 1 to 10 of about 1,195,901 (281)
On BMRN*-colouring of planar digraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 In a recent work, Bensmail, Blanc, Cohen, Havet and Rocha, motivated by applications for TDMA scheduling problems, have introduced the notion of BMRN*-colouring of digraphs, which is a type of arc-colouring with particular colouring constraints.
Julien Bensmail, Foivos Fioravantes
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Gossiping with interference in radio ring networks [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 In this paper, we study the problem of gossiping with interference constraint in radio ring networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and is expected to distribute its own message to ...
Jean-Claude Bermond +2 more
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From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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List circular backbone colouring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge.
Frederic Havet, Andrew D. King
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Constrained ear decompositions in graphs and digraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Ear decompositions of graphs are a standard concept related to several major problems in graph theory like the Traveling Salesman Problem. For example, the Hamiltonian Cycle Problem, which is notoriously N P-complete, is equivalent to deciding whether a ...
Frédéric Havet, Nicolas Nisse
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On interval number in cycle convexity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Recently, Araujo et al. [Manuscript in preparation, 2017] introduced the notion of Cycle Convexity of graphs. In their seminal work, they studied the graph convexity parameter called hull number for this new graph convexity they proposed, and they ...
Julio Araujo +3 more
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Combinatorial optimization in networks with Shared Risk Link Groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the ...
David Coudert +3 more
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Backbone colouring and algorithms for TDMA scheduling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring ...
Julien Bensmail +4 more
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Computing metric hulls in graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 We prove that, given a closure function the smallest preimage of a closed set can be calculated in polynomial time in the number of closed sets. This implies that there is a polynomial time algorithm to compute the convex hull number of a graph, when all
Kolja Knauer, Nicolas Nisse
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Improper colouring of (random) unit disk graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 For any graph $G$, the $k$-improper chromatic number $χ ^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$.
Ross J. Kang +2 more
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