The i-chords of cycles and paths
نویسنده
چکیده
An i-chord of a cycle or path is an edge whose endpoints are a distance i ≥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results include the following: A graph is strongly chordal if and only if, for i ∈ {4, 6}, every cycle C with |V (C)| ≥ i has an (i/2)-chord. A graph is a threshold graph if and only if, for i ∈ {4, 5}, every path P with |V (P )| ≥ i has an (i−2)-chord.
منابع مشابه
Characterization of signed paths and cycles admitting minus dominating function
If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.
متن کاملChorded Cycles
A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. The minimum degree and the minimum degree-sum conditions are given for a graph to contain vertex-disjoint chorded (doubly chorded) cycles containi...
متن کاملOn the outer independent 2-rainbow domination number of Cartesian products of paths and cycles
Let G be a graph. A 2-rainbow dominating function (or 2-RDF) of G is a function f from V(G) to the set of all subsets of the set {1,2} such that for a vertex v ∈ V (G) with f(v) = ∅, thecondition $bigcup_{uin N_{G}(v)}f(u)={1,2}$ is fulfilled, wher NG(v) is the open neighborhoodof v. The weight of 2-RDF f of G is the value$omega (f):=sum _{vin V(G)}|f(v)|$. The 2-rainbowd...
متن کاملExcluding cycles with a fixed number of chords
Trotignon and Vušković completely characterized graphs that do not contain cycles with exactly one chord. In particular, they show that such a graph G has chromatic number at most max(3, ω(G)). We generalize this result to the class of graphs that do not contain cycles with exactly two chords and the class of graphs that do not contain cycles with exactly three chords. More precisely we prove t...
متن کاملOn friendly index sets of cycles with parallel chords
Let G be a graph with vertex set V(G) and edge set E(G), and let A be an abelian group. A labeling f: V(G) A induces an edge labeling f"': E(G) A defined by f"'(xy) = f(x) + fey), for each edge xy e E(G). For i e A, let vt<i) = card { v e V(G) : f(v) = i} and er(i) = card ( e e E(G) : f"'(e) = i}. Let c(f) = {Iet<i) etG)1 : (i, j) e A x A}. A labeling f of a graph G is said to be A friendly if...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 32 شماره
صفحات -
تاریخ انتشار 2012