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6 papers · 2 filters
Jones' Conjecture in subcubic graphs
Marthe Bonamy, François Dross, Tomáš Masařík +3
We confirm Jones' Conjecture for subcubic graphs. Namely, if a subcubic planar graph does not contain vertex-disjoint cycles, then it suffices to delete vertices to obta…
Domination and location in twin-free digraphs
Florent Foucaud, Shahrzad Heydarshahi, Aline Parreau
A dominating set in a digraph is a set of vertices such that every vertex is either in or has an in-neighbour in . A dominating set of a digraph is locating-dominati…
New Invariants for Permutations, Orders and Graphs
Jean-christophe Aval, Nantel Bergeron, John Machacek
We study the symmetric function and polynomial combinatorial invariants of Hopf algebras of permutations, posets and graphs. We investigate their properties and the relations among…
Compacted binary trees admit a stretched exponential
Andrew Elvey Price, Wenjie Fang, Michael Wallner
A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that…
Revisiting a theorem by Folkman on graph colouring
Marthe Bonamy, Pierre Charbit, Oscar Defrain +5
We give a short proof of the following theorem due to Jon H. Folkman (1969): The chromatic number of any graph is at most plus the maximum over all subgraphs of the difference…
Tree-decorated planar maps
Luis Fredes, Avelio Sepúlveda
We introduce the set of (non-spanning) tree-decorated planar maps, and show that they are in bijection with the Cartesian product between the set of trees and the set of maps with…