Results 11 to 20 of about 563,274 (244)
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 +3 more sources
The 1 , 2 , 3-Conjecture And 1 , 2-Conjecture For Sparse Graphs
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 +2 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 +2 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{ }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 +4 more sources
Further results on an equitable 1-2-3 Conjecture [PDF]
Discrete Applied Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensmail, Julien +3 more
openaire +3 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 +3 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.
Bensmail, Julien +2 more
openaire +5 more sources
The 1–2–3 Conjecture almost holds for regular graphs [PDF]
Journal of Combinatorial Theory, Series B, 2021 15 ...
openaire +3 more sources
An Injective Version of the 1-2-3 Conjecture
Graphs and Combinatorics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensmail, Julien, Li, Bi, Li, Binlong
openaire +3 more sources
From the 1-2-3 conjecture to the Riemann hypothesis [PDF]
European Journal of Combinatorics, 2021 This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous territory of the Riemann Hypothesis. We will mostly focus on open problems, but we will also provide some simple proofs, just for adorning.
openaire +3 more sources