5 citations · 14 across the 10 of their papers we have counts for
13 papers
An 18-colour bound for locally irregular decompositions
Carla Negri Lintzmayer, Guilherme Oliveira Mota, Maycon Sambinelli +1
A graph is locally irregular if adjacent vertices have distinct degrees. A graph G is decomposable if its edge set can be decomposed into locally irregular graphs, and its locally…
Proper conflict-free 7-coloring of planar graphs
A. Jiménez, C. N. Lintzmayer, M. Sambinelli
A proper conflict-free coloring is a proper vertex coloring in which every nonisolated vertex has a color occurring uniquely in its open neighborhood. We prove that every graph wit…
Immersions of large cliques in graphs with independence number 2 and bounded maximum degree
Fábio Botler, Cristina G. Fernandes, Carla N. Lintzmayer +4
An immersion of a graph in a graph is a minimal subgraph of for which there is an injection and a set of edge-disjoint paths $\{P_e:…
On the structure of a smallest counterexample and a new class verifying the 2-Decomposition Conjecture
F. Botler, A. Jiménez, M. Sambinelli +1
The 2-Decomposition Conjecture, equivalent to the 3-Decomposition Conjecture stated in 2011 by Hoffmann-Ostenhof, claims that every connected graph with vertices of degree 2 an…
Boundedness for proper conflict-free and odd colorings
Andrea Jiménez, Kolja Knauer, Carla Negri Lintzmayer +7
The proper conflict-free chromatic number, , of a graph is the least such that has a proper -coloring in which for each non-isolated vertex there is a co…
Biclique immersions in graphs with independence number 2
Fábio Botler, Andrea Jiménez, Carla N. Lintzmayer +3
The analogue of Hadwiger's conjecture for the immersion relation states that every graph contains an immersion of . For graphs with independence number 2, this is equ…
Towards Gallai's path decomposition conjecture
Fabio Botler, Maycon Sambinelli
A path decomposition of a graph G is a collection of edge-disjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admi…
Perfect digraphs
Cândida Nunes da Silva, Orlando Lee, Maycon Sambinelli
Let be a digraph. Given a set of vertices , an -path partition of is a collection of paths of such that $\{V(P) \colon P \in \mathcal…
Decomposing split graphs into locally irregular graphs
Carla Negri Lintzmayer, Guilherme Oliveira Mota, Maycon Sambinelli
A graph is locally irregular if any pair of adjacent vertices have distinct degrees. A locally irregular decomposition of a graph is a decomposition of such t…
Gallai's path decomposition conjecture for triangle-free planar graphs
Fábio Botler, Andrea Jiménez, Maycon Sambinelli
A path decomposition of a graph is a collection of edge-disjoint paths of that covers the edge set of . Gallai (1968) conjectured that every connected graph on verti…
Berge's Conjecture and Aharoni-Hartman-Hoffman's Conjecture for locally in-semicomplete digraphs
Maycon Sambinelli, Carla Negri Lintzmayer, Cândida Nunes da Silva +1
Let be a positive integer and let be a digraph. A path partition $\sP$ of is a set of vertex-disjoint paths which covers . Its -norm is defined as $\sum_{P \in…
On Gallai's and Hajós' Conjectures for graphs with treewidth at most 3
Fábio Botler, Maycon Sambinelli, Rafael S. Coelho +1
A path (resp. cycle) decomposition of a graph is a set of edge-disjoint paths (resp. cycles) of that covers the edge set of . Gallai (1966) conjectured that every graph…
On Linial's Conjecture for Spine Digraphs
Maycon Sambinelli, Cândida Nunes da Silva, Orlando Lee
In this paper we introduce a superclass of split digraphs, which we call spine digraphs. Those are the digraphs D whose vertex set can be partitioned into two sets X and Y such tha…