DeepAI AI Chat
Log In Sign Up

On Existence of Must-Include Paths and Cycles in Undirected Graphs

by   Yefim Dinitz, et al.

Given an undirected graph G=(V,E) and vertices s,t,w_1,w_2∈ V, we study finding whether there exists a simple path P from s to t such that w_1,w_2 ∈ P. As a sub-problem, we study the question: given an undirected graph and three of its edges, does there exist a simple cycle containing all those edges? We provide necessary and sufficient conditions for the existence of such paths and cycles, and develop efficient algorithms to solve this and related problems.


page 1

page 2

page 3

page 4


Surjective polymorphisms of reflexive cycles

A reflexive cycle is any reflexive digraph whose underlying undirected g...

On the Constrained Least-cost Tour Problem

We introduce the Constrained Least-cost Tour (CLT) problem: given an und...

The Shadows of a Cycle Cannot All Be Paths

A "shadow" of a subset S of Euclidean space is an orthogonal projection ...

Simple and efficient four-cycle counting on sparse graphs

We consider the problem of counting 4-cycles (C_4) in a general undirect...

Classification of minimally unsatisfiable 2-CNFs

We consider minimally unsatisfiable 2-CNFs, i.e., minimally unsatisfiabl...

Locally EFX Allocations Over a Graph

The fairness notion of envy-free up to any good (EFX) has recently gaine...