2014
DOI: 10.1137/130940499
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On Packing Two Graphs with Bounded Sum of Sizes and Maximum Degree

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Cited by 2 publications
(5 citation statements)
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“…In this case, two edge disjoint copies of a graph G are placed into K n with the additional property that two copies of the same vertex must be mapped to different vertices in K n . In [9], Schuster's result is used to prove a necessary condition for packing two graphs with given maximum and average degrees.…”
Section: Theorem 4 ([1]mentioning
confidence: 99%
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“…In this case, two edge disjoint copies of a graph G are placed into K n with the additional property that two copies of the same vertex must be mapped to different vertices in K n . In [9], Schuster's result is used to prove a necessary condition for packing two graphs with given maximum and average degrees.…”
Section: Theorem 4 ([1]mentioning
confidence: 99%
“…Though this paper focuses on extending classical packing results to the list setting, one of our goals is to provide tools to handle problems of standard graph packings. In particular, we heavily use Theorems 5 and 6 in [3] to get an approximate solution to a conjecture oḟ Zak [9] on packing n-vertex graphs with given sizes and maximum degrees.…”
Section: Introductionmentioning
confidence: 99%
“…So by (3) and the minimality of G, triple G packs, and this packing extends to G by placing v 1 on w 1 and v 2 on w 2 . Therefore, s ≥ 3 and the average degree of H is at least 4 3 . In fact, since H was the smallest tree component, all of G 1 has average degree at least 4/3.…”
Section: Case 22mentioning
confidence: 99%
“…(R2) Each vertex x adjacent to 1-vertices (it must be in V 1 and have degree at least 3K) gives to each z ∈ L(x) charge 4 3 and to each z ∈ N (x) − L(x) charge…”
Section: Weak Vertices and Sponsorsmentioning
confidence: 99%
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