A characterization of uniquely representable interval graphs
نویسندگان
چکیده
منابع مشابه
Unique Perfect Phylogeny Characterizations via Uniquely Representable Chordal Graphs
The perfect phylogeny problem is a classic problem in computational biology, where we seek an unrooted phylogeny that is compatible with a set of qualitative characters. Such a tree exists precisely when an intersection graph associated with the character set, called the partition intersection graph, can be triangulated using a restricted set of fill edges. Semple and Steel used the partition i...
متن کاملUniquely Restricted Matchings in Interval Graphs
A matching M in a graph G is said to be uniquely restricted if there is no other matching in G that matches the same set of vertices as M . We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted matching in an interval graph, thereby answering a question of Golumbic et al. (“Uniquely restricted matchings”, M. C. Golumbic, T. Hirst and M. Lewenstein, Algorit...
متن کاملSolis Graphs and Uniquely Metric Basis Graphs
A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish...
متن کاملCharacterization of Uniquely Colorable and Perfect Graphs
This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The main results are 1) Every uniquely k-colorable graph is (k 1)-connected. 2) If G is a uniquely k-colorable graph, then (G) ≥ k l. 3) A maximal planar graph G of order 3 or more has chromatic number 3 if and only if G is Eulerian. 4) Every interval graph is perfect. 5) A graph G is chordal if and only if G can b...
متن کاملAlgebraic characterization of uniquely vertex colorable graphs
The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-colorability of a graph G is equivalent to the condition 1 ∈ IG,k for a certain ideal IG,k ⊆ k[x1, . . . , xn]. In this paper, we extend this result by proving a general decomposition theorem for IG,k . This theorem allows us to giv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1985
ISSN: 0166-218X
DOI: 10.1016/0166-218x(85)90072-1