# The Phylogeny Graphs of Doubly Partial Orders

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 4, page 657-664
- ISSN: 2083-5892

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topBoram Park, and Yoshio Sano. "The Phylogeny Graphs of Doubly Partial Orders." Discussiones Mathematicae Graph Theory 33.4 (2013): 657-664. <http://eudml.org/doc/267778>.

@article{BoramPark2013,

abstract = {The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph P(D) of a digraph D is the (simple undirected) graph defined by V (P(D)) := V (D) and E(P(D)) := \{xy | N+D (x) ∩ N+D(y) ¹ ⊘ \} ⋃ \{xy | (x,y) ∈ A(D)\}, where N+D(x):= \{v ∈ V(D) | (x,v) ∈ A (D)\}. In this note, we show that the phylogeny graph of a doubly partial order is an interval graph. We also show that, for any interval graph G̃, there exists an interval graph G such that G̃ contains the graph G as an induced subgraph and that G̃ is the phylogeny graph of a doubly partial order.},

author = {Boram Park, Yoshio Sano},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {competition graph; phylogeny graph; doubly partial order; interval graph},

language = {eng},

number = {4},

pages = {657-664},

title = {The Phylogeny Graphs of Doubly Partial Orders},

url = {http://eudml.org/doc/267778},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Boram Park

AU - Yoshio Sano

TI - The Phylogeny Graphs of Doubly Partial Orders

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 4

SP - 657

EP - 664

AB - The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph P(D) of a digraph D is the (simple undirected) graph defined by V (P(D)) := V (D) and E(P(D)) := {xy | N+D (x) ∩ N+D(y) ¹ ⊘ } ⋃ {xy | (x,y) ∈ A(D)}, where N+D(x):= {v ∈ V(D) | (x,v) ∈ A (D)}. In this note, we show that the phylogeny graph of a doubly partial order is an interval graph. We also show that, for any interval graph G̃, there exists an interval graph G such that G̃ contains the graph G as an induced subgraph and that G̃ is the phylogeny graph of a doubly partial order.

LA - eng

KW - competition graph; phylogeny graph; doubly partial order; interval graph

UR - http://eudml.org/doc/267778

ER -

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