7 papers
On Strong Majority Edge Colourings with Few Colours
Paweł Pękała, Jakub Przybyło
A strong majority edge colouring of a graph is an edge colouring in which, for every edge and every colour , at most half the edges adjacent to receive colour . L…
Asymptotically Tight Bound for the Conflict-Free Chromatic Index
Mateusz Kamyczura, Jakub PrzybyÅo
The conflict-free chromatic index of a graph is the minimum number of colours in an edge colouring of such that the neighbourhood of every edge contains a colour appearing…
On asymptotically tight bounds for the open conflict-free chromatic indexes of nearly regular graphs
Mateusz Kamyczura, Jakub PrzybyÅo
An edge colouring of a graph is called conflic-free if every non-isolated edge of has a uniquely coloured neighbour in its open edge neighbourhood. The least number of…
Degree-balanced decompositions of cubic graphs
Borut Lužar, Jakub PrzybyÅo, Roman Soták
We show that every cubic graph on vertices contains a spanning subgraph in which the number of vertices of each degree deviates from by at most , up…
On list extensions of the majority edge colourings
PaweÅ PÄkaÅa, Jakub PrzybyÅo
We investigate possible list extensions of generalised majority edge colourings of graphs and provide several results concerning these. Given a graph , a list assignment $…
Alon-Tarsi for hypergraphs
Marcin Anholcer, Bartłomiej Bosek, BartÅomiej Bosek +12
Given a hypergraph , define for every edge a linear expression with arguments corresponding to the vertices. Next, let the polynomial be the product of such…