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Traceability in { K 1 , 4 , K 1 , 4 + e } -free graphs

Wei Zheng;  Ligong Wang — 2019

Czechoslovak Mathematical Journal

A graph G is called { H 1 , H 2 , ⋯ , H k } -free if G contains no induced subgraph isomorphic to any graph H i , 1 ≤ i ≤ k . We define σ k = min ∑ i = 1 k d ( v i ) : { v 1 , ⋯ , v k } is an independent set of vertices in G . In this paper, we prove that (1) if G is a connected { K 1 , 4 , K 1 , 4 + e } -free graph of order n and σ 3 ( G ) ≥ n - 1 , then G is traceable, (2) if G is a 2-connected { K 1 , 4 , K 1 , 4 + e } -free graph of order n and | N ( x 1 ) ∪ N ( x 2 ) | + | N ( y 1 ) ∪ N ( y 2 ) | ≥ n - 1 for any two distinct pairs of non-adjacent vertices { x 1 , x 2 } , { y 1 , y 2 } of G , then G is traceable, i.e., G has a Hamilton path, where K 1 , 4 + e is a graph obtained by joining a pair of non-adjacent vertices in a K 1 , 4 .

Division schemes under uncertainty of claims

Xianghui Li;  Yang Li;  Wei Zheng — 2021

Kybernetika

In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with...

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