Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Heuvel, Jan van den"'
Autor:
Heuvel, Jan van den, Xu, Xinyi
If a graph is $n$-colourable, then it obviously is $n'$-colourable for any $n'\ge n$. But the situation is not so clear when we consider multi-colourings of graphs. A graph is $(n,k)$-colourable if we can assign each vertex a $k$-subset of $\{1,2,\ld
Externí odkaz:
http://arxiv.org/abs/2407.05730
Autor:
Heuvel, Jan van den, Kierstead, H. A.
The generalized coloring numbers col_r(G) (also denoted by scol_r(G)) and wcol_r(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring number, and have found important theoretical and algorithmic applications
Externí odkaz:
http://arxiv.org/abs/1907.12149
Autor:
Eickmeyer, Kord, Heuvel, Jan van den, Kawarabayashi, Ken-ichi, Kreutzer, Stephan, de Mendez, Patrice Ossona, Pilipczuk, Michał, Quiroz, Daniel A., Rabinovich, Roman, Siebertz, Sebastian
We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but it does b
Externí odkaz:
http://arxiv.org/abs/1812.08003
Autor:
Heuvel, Jan van den, Wood, David R.
Publikováno v:
J. London Math. Society 98.1:129-148, 2018
Hadwiger's Conjecture asserts that every $K_t$-minor-free graph has a proper $(t-1)$-colouring. We relax the conclusion in Hadwiger's Conjecture via improper colourings. We prove that every $K_t$-minor-free graph is $(2t-2)$-colourable with monochrom
Externí odkaz:
http://arxiv.org/abs/1704.06536
Autor:
Heuvel, Jan van den, Kreutzer, Stephan, Pilipczuk, Michał, Quiroz, Daniel A., Rabinovich, Roman, Siebertz, Sebastian
A successor-invariant first-order formula is a formula that has access to an auxiliary successor relation on a structure's universe, but the model relation is independent of the particular interpretation of this relation. It is well known that succes
Externí odkaz:
http://arxiv.org/abs/1701.08516
For any graph $G=(V,E)$ and positive integer $p$, the exact distance-$p$ graph $G^{[\natural p]}$ is the graph with vertex set $V$, which has an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance $p$ in $G$. For odd $p$, Ne\v{
Externí odkaz:
http://arxiv.org/abs/1612.02160
Autor:
Heuvel, Jan van den, de Mendez, Patrice Ossona, Quiroz, Daniel, Rabinovich, Roman, Siebertz, Sebastian
The generalised colouring numbers $\mathrm{col}_r(G)$ and $\mathrm{wcol}_r(G)$ were introduced by Kierstead and Yang as a generalisation of the usual colouring number, and have since then found important theoretical and algorithmic applications. In t
Externí odkaz:
http://arxiv.org/abs/1602.09052
Autor:
Edwards, Katherine, Girão, António, Heuvel, Jan van den, Kang, Ross J., Puleo, Gregory J., Sereni, Jean-Sébastien
We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\Del
Externí odkaz:
http://arxiv.org/abs/1407.4339
Autor:
Heuvel, Jan van den
Publikováno v:
In: S.R. Blackburn, S. Gerke and M. Wildon (eds.), "Surveys in Combinatorics 2013". Cambridge UP, 2013
Many combinatorial problems can be formulated as "Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?". An example of such a question is: given two k-colourings of a graph, can I transform the first k-co
Externí odkaz:
http://arxiv.org/abs/1312.2816
We study the following problem: given a real number k and integer d, what is the smallest epsilon such that any fractional (k+epsilon)-precoloring of vertices at pairwise distances at least d of a fractionally k-colorable graph can be extended to a f
Externí odkaz:
http://arxiv.org/abs/1205.5405