Generalizing $p$-goodness to ordered graphs

TL;DR

This paper explores which ordered trees maintain their $p$-goodness property across all values of $p$, extending known results from unconnected graphs to ordered structures.

Contribution

It introduces the concept of order-$p$-goodness for ordered trees and investigates which of these trees preserve this property for all $p$, expanding the understanding of graph goodness.

Findings

Identifies classes of ordered trees that are order-$p$-good for all $p$

Extends the concept of $p$-goodness from unconnected to ordered graphs

Provides characterization results for ordered trees with this property

Abstract

It is known that the connected graphs that are $p$-good for all $p$ are the trees. In this paper, we ask which ordered trees are order-$p$-good for all $p$.