Extremal Graphs for a Graph Packing Theorem of Sauer and Spencer
نویسندگان
چکیده
Let G1 and G2 be graphs of order n with maximum degree ∆1 and ∆2, respectively. G1 and G2 are said to pack if there exist injective mappings of the vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer showed that if ∆1∆2 < n 2 , then G1 and G2 pack. We extend this result by showing that if ∆1∆2 ≤ n2 , then G1 and G2 do not pack if and only if one of G1 or G2 is a perfect matching and the other either is Kn 2 , n 2 with n2 odd or contains Kn 2 +1 .
منابع مشابه
Extremal Theorems for Degree Sequence Packing and the Two-Color Discrete Tomography Problem
A sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} such that the degree of vi is di. We say that graphic sequences π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) pack if there exist edge-disjoint n-vertex graphs G1 and G2 such that for j ∈ {1, 2}, dGj (vi) = d (j) i for all i ∈ {1, . . . , n}. Here, we prove several ...
متن کاملExtremal Theorems for Degree Sequence Packing and the 2-Color Discrete Tomography Problem
A sequence π = (d1, . . . , dn) is graphic if there is a simple graph G with vertex set {v1, . . . , vn} such that the degree of vi is di. We say that graphic sequences π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) pack if there exist edge-disjoint n-vertex graphs G1 and G2 such that for j ∈ {1, 2}, dGj (vi) = d (j) i for all i ∈ {1, . . . , n}. Here, we prove several ...
متن کاملThe Signless Laplacian Estrada Index of Unicyclic Graphs
For a simple graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$, where $q^{}_1, q^{}_2, dots, q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...
متن کاملEccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
متن کاملExtremal and Probabilistic Combinatorics
09:20 – 09:30 Opening remarks 09:30 – 10:00 Dhruv Mubayi Quasirandom hypergraphs 10:05 – 10:35 Yufei Zhao Sparse regularity and counting in pseudorandom graphs 10:35 – 11:15 Coffee 11:15 – 11:45 Asaf Shapira Exact bounds for some hypergraph saturation problems 11:50 – 12:20 Po-Shen Loh Computing with voting trees 12:20 – 14:30 Lunch 14:30 – 15:00 Joel Spencer Six standard deviations still suffi...
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:
- Combinatorics, Probability & Computing
دوره 16 شماره
صفحات -
تاریخ انتشار 2007