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The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs
Maria Axenovich, Jonathan Rollin, Torsten Ueckerdt
An ordered graph is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples with . For a positive integer , a matrix $M \in \mat…
The -strong induced arboricity of a graph
Maria Axenovich, Daniel Goncalves, Jonathan Rollin +1
The induced arboricity of a graph is the smallest number of induced forests covering the edges of . This is a well-defined parameter bounded from above by the number of edge…
Regular colorings and factors of regular graphs
Anton Bernshteyn, Omid Khormali, Ryan R. Martin +4
An -coloring of an -regular graph is an edge coloring such that each vertex is incident to edges of one color and edge of a different color. In this paper…
Chromatic number of ordered graphs with forbidden ordered subgraphs
Maria Axenovich, Jonathan Rollin, Torsten Ueckerdt
It is well-known that the graphs not containing a given graph H as a subgraph have bounded chromatic number if and only if H is acyclic. Here we consider ordered graphs, i.e., grap…