Search Results - "SOPENA, Eric"

Homomorphisms of signed graphs: An update by Naserasr, Reza, Sopena, Éric, Zaslavsky, Thomas

“…A signed graph is a graph together with an assignment of signs to the edges. A closed walk in a signed graph is said to be positive (negative) if it has an…”
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Strong incidence colouring of graphs by Benmedjdoub, Brahim, Sopena, Éric

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i-Mark: A new subtraction division game by Sopena, Eric

“…Given two finite sets of integers S⊆N∖{0} and D⊆N∖{0,1}, the impartial combinatorial game i-Mark(S,D) is played on a heap of tokens. From a heap of n tokens,…”
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On the oriented achromatic number of graphs by P.D., Pavan, Sopena, Éric

“…The oriented achromatic number of an oriented graph G⃗, denoted ψo(G⃗), is the largest n such that G⃗ admits a complete oriented n-colouring. If G is an…”
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Homomorphisms of Signed Graphs by Naserasr, Reza, Rollová, Edita, Sopena, Éric

“…A signed graph [G,Σ] is a graph G together with an assignment of signs + and − to all the edges of G where Σ is the set of negative edges. Furthermore [G,Σ1]…”
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Proper connection and proper-walk connection of digraphs by Fiedorowicz, Anna, Sidorowicz, Elżbieta, Sopena, Éric

“…An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices (u,v), the digraph D contains a directed path (a directed…”
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Complete oriented colourings and the oriented achromatic number by Sopena, Eric

“…In this paper, we initiate the study of complete colourings of oriented graphs and the new associated notion of the oriented achromatic number of oriented and…”
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Every planar graph with Δ ${\rm{\Delta }}$ ⩾ 8 is totally (Δ+2) $({\rm{\Delta }}+2)$‐choosable by Bonamy, Marthe, Pierron, Théo, Sopena, Éric

“…Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally k $k$‐choosable if for any list assignment of…”
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On the broadcast independence number of locally uniform 2-lobsters by Ahmane, Messaouda, Bouchemakh, Isma, Sopena, Éric

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A Proof of the Multiplicative 1-2-3 Conjecture by Bensmail, Julien, Hocquard, Hervé, Lajou, Dimitri, Sopena, Éric

“…We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kaziów in 2012, is true. Namely, for every connected graph with order at…”
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Homomorphisms of Sparse Signed Graphs by Charpentier, Clément, Naserasr, Reza, Sopena, Éric

“…The notion of homomorphism of signed graphs, introduced quite recently, provides better interplay with the notion of minor and is thus of high importance in…”
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Generalising the achromatic number to Zaslavsky's colourings of signed graphs by Bensmail, Julien, Dross, François, Oijid, Nacim, Sopena, Éric

“…The chromatic number, which refers to the minimum number of colours required to colour the vertices of graphs properly, is one of the most central notions of…”
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Further evidence towards the multiplicative 1-2-3 Conjecture by Bensmail, Julien, Hocquard, Hervé, Lajou, Dimitri, Sopena, Éric

“…The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kaziów in 2012, states that, a few obvious exceptions apart, all graphs can be…”
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On a List Variant of the Multiplicative 1-2-3 Conjecture by Bensmail, Julien, Hocquard, Hervé, Lajou, Dimitri, Sopena, Éric

“…The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with 1, 2, 3 so that no two adjacent vertices are incident to the same sum of…”
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On the signed chromatic number of some classes of graphs by Bensmail, Julien, Das, Sandip, Nandi, Soumen, Pierron, Théo, Sen, Sagnik, Sopena, Éric

“…A signed graph (G,σ) is a graph G along with a function σ:E(G)→{+,−}. A closed walk of a signed graph is positive (resp., negative) if it has an even (resp.,…”
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Exact square coloring of subcubic planar graphs by Foucaud, Florent, Hocquard, Hervé, Mishra, Suchismita, Narayanan, Narayanan, Naserasr, Reza, Sopena, Éric, Valicov, Petru

“…We study the exact square chromatic number of subcubic planar graphs. An exact square coloring of a graph G is a vertex-coloring in which any two vertices at…”
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Outerplanar and Planar Oriented Cliques by Nandy, Ayan, Sen, Sagnik, Sopena, Éric

“…The clique number of an undirected graph G is the maximum order of a complete subgraph of G and is a well‐known lower bound for the chromatic number of G…”
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Packing Coloring of Some Undirected and Oriented Coronae Graphs by Laïche, Daouya, Bouchemakh, Isma, Sopena, Éric

“…The packing chromatic number χ ) of a graph is the smallest integer such that its set of vertices ) can be partitioned into disjoint subsets , . . . , , in…”
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Pushable chromatic number of graphs with degree constraints by Bensmail, Julien, Das, Sandip, Nandi, Soumen, Paul, Soumyajit, Pierron, Théo, Sen, Sagnik, Sopena, Éric

“…Pushable homomorphisms and the pushable chromatic number χp of oriented graphs were introduced by Klostermeyer and MacGillivray in 2004. They notably observed…”
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On the complexity of determining the irregular chromatic index of a graph by Baudon, Olivier, Bensmail, Julien, Sopena, Éric

“…An undirected simple graph G is locally irregular if adjacent vertices of G have different degrees. An edge-colouring ϕ of G is locally irregular if each…”
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