Nathan Bowler,Christian Elbracht,Joshua Erde et al.
Nathan Bowler et al.
A graph G is said to be ≼-ubiquitous, where ≼ is the minor relation between graphs, if whenever Γ is a graph with nG≼Γ for all n∈N, then one also has ℵ0G≼Γ, where αG is the disjoint un...
Locally common graphs [0.03%]
局部常见的图
Endre Csóka,Tamás Hubai,László Lovász
Endre Csóka
Goodman proved that the sum of the number of triangles in a graph on n nodes and its complement is at least n 3 ∕ 24 ; in other words, this sum is minimized, asymptotically, by a random graph with edge density 1/2. Erdős conje...
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups [0.03%]
无限交换群的4正则凯莱图的哈密顿分解
Joshua Erde,Florian Lehner
Joshua Erde
A well-known conjecture of Alspach says that every 2 k -regular Cayley graph of a finite abelian group can be decomposed into Hamiltonian cycles. We consider an analogous question for infinite abelian groups. In this setting one natura...
Ewan Davies,Rémi de Joannis de Verclos,Ross J Kang et al.
Ewan Davies et al.
Given ε > 0 , there exists f 0 such that, if f 0 ≤ f ≤ Δ 2 + 1 , then for any graph G on n vertices of maximum degree Δ in which the neighbourhood of every vertex in G spans at most Δ 2 ∕ f edges, (i)a...
Single-conflict colouring [0.03%]
单冲突着色问题
Zdeněk Dvořák,Louis Esperet,Ross J Kang et al.
Zdeněk Dvořák et al.
Given a multigraph, suppose that each vertex is given a local assignment of k colours to its incident edges. We are interested in whether there is a choice of one local colour per vertex such that no edge has both of its local colours chose...
Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture [0.03%]
平面三次图的汉密尔顿圈和Barnette猜想的新部分证明
Behrooz Bagheri Gh,Tomas Feder,Herbert Fleischner et al.
Behrooz Bagheri Gh et al.
We study the existence of hamiltonian cycles in plane cubic graphs G having a facial 2-factor Q . Thus hamiltonicity in G is transformed into the existence of a (quasi) spanning tree of faces in the contraction G ∕ Q . In particular, ...
Bart Litjens
Bart Litjens
Let Γ be a multigraph with for each vertex a cyclic order of the edges incident with it. For n ≥ 3 , let D 2 n be the dihedral group of order 2 n . Define D ≔ { ( ± 1 a 0 1 ) ∣ a ∈ Z } . Goodall et a...
M Mnich,E Teutrine
M Mnich
We study feedback vertex sets (FVS) in tournaments, which are orientations of complete graphs. As our main result, we show that any tournament on n nodes has at most 1.5949 n minimal FVS. This significantly improves the previously best uppe...
Henry Liu,Oleg Pikhurko,Teresa Sousa
Henry Liu
Let G be a graph whose edges are colored with k colors, and H=(H1,⋯,Hk) be a k-tuple of graphs. A monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic c...