منابع مشابه
Minimum degree games for graphs
Given δ and n, a minimum degree game starts with n disconnected nodes. Two players alternate, each adding a new edge in turn, until the resulting graph has minimum degree at least δ. In the achievement game, the last player to move is the winner; in the avoidance game, the last to play is the loser. We determine a winning strategy for the avoidance game for every δ and n. The achievement game i...
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The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
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For a fixed multigraph H with vertices w1, . . . , wm, a graph G is H-linked if for every choice of vertices v1, . . . , vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs. Given a connected multigraph H with k edges and minimum degree at least two and n 7.5k, we...
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We write H → G if every 2-coloring of the edges of graph H contains a monochromatic copy of graph G. A graph H is G-minimal if H → G, but for every proper subgraph H ′ of H, H ′ 6→ G. We define s(G) to be the minimum s such that there exists a G-minimal graph with a vertex of degree s. We prove that s(Kk) = (k − 1) and s(Ka,b) = 2 min(a, b) − 1. We also pose several related open problems. c © 2...
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The main result of this paper is as follows: Let G be a graph and m a positive integer such that (i) |V (G)| ≥ 4m+1, (ii) δ(G) ≥ |V (G)| 2 +1. For any subset {e1, . . . , em+1} of E(G), the graph G − {e1, . . . , em} possesses a 2-factor containing em+1. The above Theorem also yields a Dirac type sufficient condition for a graph to be magic. All graphs considered are assumed to be simple and fi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90109-0