منابع مشابه
A New Characterization of P4-connected Graphs
A graph is said to be P 4-connected if for every partition of its vertex-set into two nonempty disjoint sets, some P 4 in the graph has vertices from both sets in the partition. A P 4-chain is a sequence of vertices such that every four consecutive ones induce a P 4. The main result of this work states that a graph is P 4-connected if and only if each pair of vertices is connected by a P 4-chai...
متن کامل2-Factors in r-Connected {K1,k, P4}-Free Graphs
In [3], Faudree et.al. considered the proposition “Every {X, Y }-free graph of sufficiently large order has a 2-factor,” and they determined those pairs {X, Y } which make this proposition true. Their result says that one of them is {X, Y } = {K1,4, P4}. In this paper, we investigate the existence of 2-factors in r-connected {K1,k, P4}-free graphs. We prove that if r ≥ 1 and k ≥ 2, and if G is ...
متن کاملExtremal P4-stable graphs
Call a graph G k-stable (with respect to some graph H) if, deleting any k edges of G, the remaining graph still contains H as a subgraph. For a fixed H, the minimum number of edges in a k-stable graph is denoted by S(k). We prove general bounds on S(k) and compute the exact value of the function S(k) for H = P4. The main result can be applied to extremal k-edge-hamiltonian hypergraphs.
متن کاملTree-like Decompositions of Simply Connected Domains
We show that any simply connected rectifiable domain Ω can be decomposed into Lipschitz crescents using only crosscuts of the domain and using total length bounded by a multiple of the length of ∂Ω. In particular, this gives a new proof of a theorem of Peter Jones that such a domain can be decomposed into Lipschitz disks. 1991 Mathematics Subject Classification. Primary: 68U05 Secondary: 26B15,...
متن کاملTree-like partial Hamming graphs
Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227–240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00088-0