Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A new problem related to Eulerian graphs

Marcin Stawiski

Abstract

Let $G$ be a graph, and $H$ be a finite subgraph of $G$. We say that $H$ is a (semi) $S$-Eulerian subgraph if there exists a closed (open) trail $T$ in $G$ such that each edge of $H$ appears in $T$. We show that the problem of determining whether a subgraph $H$ of a finite graph $G$ is (semi) $S$-Eulerian is NP-Complete. Moreover, we show that both versions of the problem become linear in time if we restrict ourselves to connected subgraphs $H$.

A new problem related to Eulerian graphs

Abstract

Let be a graph, and be a finite subgraph of . We say that is a (semi) -Eulerian subgraph if there exists a closed (open) trail in such that each edge of appears in . We show that the problem of determining whether a subgraph of a finite graph is (semi) -Eulerian is NP-Complete. Moreover, we show that both versions of the problem become linear in time if we restrict ourselves to connected subgraphs .
Paper Structure (2 sections, 5 theorems)

This paper contains 2 sections, 5 theorems.

Table of Contents

  1. Introduction
  2. Main results

Key Result

Theorem 1

The problem of determining whether a given subgraph $H$ of a finite graph $G$ is (semi) $S$-Eulerian is NP-Complete.

Theorems & Definitions (8)

  • Theorem 1
  • Theorem 2
  • Conjecture 3
  • Theorem 4: Garey, Johnson, Stockmeyer 1976 Garey
  • Theorem 5
  • proof
  • Theorem 6
  • proof