Results 11 to 20 of about 159,016,183 (278)
The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2014 The 1, 2, 3-Conjecture states that the edges of a graph without isolated edges can be labeled from {1, 2, 3} so that the sums of labels at adjacent vertices are distinct.
Cranston Daniel W. +2 more
doaj +4 more sources
A Proof of the Multiplicative 1-2-3 Conjecture [PDF]
Combinatorica, 2022 We prove that the product version of the 1-2-3 Conjecture, raised by Skowronek-Kazi{ó}w in 2012, is true. Namely, for every connected graph with order at least 3, we prove that we can assign labels 1,2,3 to the edges in such a way that no two adjacent vertices are incident to the same product of labels.
Bensmail, Julien +3 more
openaire +4 more sources
Further evidence towards the multiplicative 1-2-3 Conjecture [PDF]
Discrete Applied Mathematics, 2022 The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kazi{ó}w in 2012, states that, a few obvious exceptions apart, all graphs can be 3-edge-labelled so that no two adjacent vertices get incident to the same product of labels. To date, this conjecture was mainly verified for complete graphs and 3-colourable graphs.
Bensmail, Julien +3 more
openaire +7 more sources
An Oriented Version of the 1-2-3 Conjecture
Discussiones Mathematicae Graph Theory, 2015 The well-known 1-2-3 Conjecture addressed by Karoński, Luczak and Thomason asks whether the edges of every undirected graph G with no isolated edge can be assigned weights from {1, 2, 3} so that the sum of incident weights at each vertex yields a proper ...
Baudon Olivier +2 more
doaj +5 more sources
On a List Variant of the Multiplicative 1-2-3 Conjecture
Graphs and Combinatorics, 2022 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 labels. In the last decades, several aspects of this problem have been studied in literature, including more general versions and slight variations.
Bensmail, Julien +3 more
openaire +5 more sources
A 1-2-3-4 result for the 1-2-3 conjecture in 5-regular graphs [PDF]
Discrete Applied Mathematics, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akbar Davoodi, Leila Maherani
core +9 more sources
Going Wide with the 1-2-3 Conjecture
Discrete Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensmail, Julien +2 more
openaire +5 more sources
Decomposability of graphs into subgraphs fulfilling the 1–2–3 Conjecture [PDF]
Discrete Applied Mathematics, 2019 The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general. We prove that every $d$-regular graph, $d\geq 2$, can be decomposed into at most $2$ subgraphs (without isolated edges) fulfilling the 1 ...
Julien Bensmail, Jakub Przybylo
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Bounding the monomial index and (1,l)-weight choosability of a graph [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Ben Seamone
doaj +4 more sources
On the role of 3s for the 1-2-3 Conjecture [PDF]
Theoretical Computer Science, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Julien Bensmail +2 more
openaire +6 more sources