8 papers
Not All Degree Constraints Are Created Equal when Computing Spanning Trees
Narek Bojikian, Alexander Firbas, Robert Ganian +2
We study the computation of minimum spanning trees subject to local degree constraints. Recent work (ICALP 2026) established that three natural formalizations of this problem share…
How Close is a Tree to a Euclidean Minimum Spanning Tree?
Todor AntiÄ, JiÅà Fiala, Jelena GliÅ¡iÄ +8
Let be a straight-line crossing-free drawing of a tree . A \emph{bad pair} in is a pair of non-adjacent vertices of whose Euclidean distance in is smaller tha…
Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees
Narek Bojikian, Alexander Firbas, Robert Ganian +2
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph and a constraint function , we ask for a (minimu…
A Polynomial Kernel for Face Cover on Non-Embedded Planar Graphs
Thekla Hamm, Sukanya Pandey, Krisztina Szilágyi
Given a planar graph, a subset of its vertices called terminals, and , the Face Cover Number problem asks whether the terminals lie on the boundaries of at most $…
Pathfinding in Self-Deleting Graphs
Michal DvoÅák, DuÅ¡an Knop, Michal Opler +3
In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we st…
Density of Traceable Graphs
Michal DvoÅák, DuÅ¡an Knop, Michal Opler +3
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show…