Construction of Sc Chordal and Sc Weakly Chordal Graphs
نویسندگان
چکیده
منابع مشابه
What Is between Chordal and Weakly Chordal Graphs?
An (h, s, t)-representation of a graph G consists of a collection of subtrees {Sv |v ∈ V (G)} of a tree T , such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [∞...
متن کاملIntersection models of weakly chordal graphs
We first present new structural properties of a two-pair in various graphs. A twopair is used in a well-known characterization of weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K2,3, 4P2, P2 ∪ P4, P6,H1,H2,H3)-free graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the ...
متن کاملNew Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs
A distance-k matching in a graph G is matching M in which the distance between any two edges of M is at least k. A distance-2 matching is more commonly referred to as an induced matching. In this paper, we show that when G is weakly chordal, the size of the largest induced matching in G is equal to the minimum number of co-chordal subgraphs of G needed to cover the edges of G, and that the co-c...
متن کاملChordal Graphs
One can prove the following propositions: (1) For every non zero natural number n holds n − 1 is a natural number and 1 ≤ n. (2) For every odd natural number n holds n − 1 is a natural number and 1 ≤ n. (3) For all odd integers n, m such that n < m holds n ≤ m − 2. (4) For all odd integers n, m such that m < n holds m + 2 ≤ n. (5) For every odd natural number n such that 1 6= n there exists an ...
متن کاملAcyclic Colorings and Triangulations of Weakly Chordal Graphs
An acyclic coloring of a graph is a proper vertex coloring without bichromatic cycles. We show that the acyclic colorings of any weakly chordal graph G correspond to the proper colorings of triangulations of G. As a consequence, we obtain polynomial-time algorithms for the acyclic coloring problem and the perfect phylogeny problem on the class of weakly chordal graphs. Our results also imply li...
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: American Journal of Applied Mathematics
سال: 2016
ISSN: 2330-0043
DOI: 10.11648/j.ajam.20160403.17